You need to use a union.

Off the top of my head:

all_settings="{{ foo|map(attribute='settings')|union(bar|map(attribute='settings')) }}"

loop requires a valid list. But we got here is,

[({'i_am': 'sam', 'eggs_ham': '456'}, AnsibleUndefined),
 ({'i_am': 'sam', 'eggs_ham': 'ham'}, {'transport': 'train'}),
 ({'i_am': 'eggs', 'eggs_ham': '456'}, AnsibleUndefined)]

Since no value is assigned to transport_fact_results when common_thing_2 is not defined.

if you remove the when condition it will work.

CODE:

- hosts: localhost
  vars:
    default_thing_1: 123
    default_thing_2: 456
    default_transport: train
    list_of_things:
      - name: foo
        common_thing_1: "sam"
      - name: bar
        common_thing_1: "sam"
        common_thing_2: "ham"
      - name: biz
        common_thing_1: "eggs"
  tasks:
    - name: Set the Things Facts
      set_fact:
        thing:
          i_am: "{{ item.common_thing_1 | default(default_thing_1) }}"
          eggs_ham: "{{ item.common_thing_2 | default(default_thing_2) }}"
      loop: "{{ list_of_things }}"
      register: things_fact_results
    - name: Set Optional Things Facts
      set_fact:
        thing:
          transport: "{{ item.transport | default(default_transport) }}"
      when: "item.common_thing_2 is defined and item.common_thing_2 == 'ham'"
      loop: "{{ list_of_things }}"
      register: transport_fact_results
    - name: Debug the Facts
      debug:
        msg: "{{ item.0 | combine(item.1|default({})) }}"
      loop: "{{
        things_fact_results.results |
        map(attribute='ansible_facts.thing') | list |
        zip(
          transport_fact_results.results |
          map(attribute='ansible_facts.thing') | list
        ) | list
      }}"

OUTPUT:

PLAY [localhost] ************************************************************************************************************************************************************************************************

TASK [Gathering Facts] ******************************************************************************************************************************************************************************************
ok: [localhost]

TASK [Set the Things Facts] *************************************************************************************************************************************************************************************
ok: [localhost] => (item={u'common_thing_1': u'sam', u'name': u'foo'})
ok: [localhost] => (item={u'common_thing_1': u'sam', u'common_thing_2': u'ham', u'name': u'bar'})
ok: [localhost] => (item={u'common_thing_1': u'eggs', u'name': u'biz'})

TASK [Set Optional Things Facts] ********************************************************************************************************************************************************************************
ok: [localhost] => (item={u'common_thing_1': u'sam', u'name': u'foo'})
ok: [localhost] => (item={u'common_thing_1': u'sam', u'common_thing_2': u'ham', u'name': u'bar'})
ok: [localhost] => (item={u'common_thing_1': u'eggs', u'name': u'biz'})

TASK [Debug the Facts] ******************************************************************************************************************************************************************************************
ok: [localhost] => (item=[{u'eggs_ham': u'456', u'i_am': u'sam'}, {u'transport': u'train'}]) => {
    "msg": {
        "eggs_ham": "456", 
        "i_am": "sam", 
        "transport": "train"
    }
}
ok: [localhost] => (item=[{u'eggs_ham': u'ham', u'i_am': u'sam'}, {u'transport': u'train'}]) => {
    "msg": {
        "eggs_ham": "ham", 
        "i_am": "sam", 
        "transport": "train"
    }
}
ok: [localhost] => (item=[{u'eggs_ham': u'456', u'i_am': u'eggs'}, {u'transport': u'train'}]) => {
    "msg": {
        "eggs_ham": "456", 
        "i_am": "eggs", 
        "transport": "train"
    }
}

PLAY RECAP ******************************************************************************************************************************************************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0  

You can get most of what you want using the combine filter, like this:

- hosts: localhost
  gather_facts: false
  tasks:
    - set_fact:
        dict3: "{{ dict1|combine(dict2, list_merge='append') }}"

    - debug:
        var: dict3

This will produce:

TASK [debug] *******************************************************************
ok: [localhost] => {
    "dict3": {
        "poc-cu2": [
            "40:A6:B7:5E:22:11",
            "40:A6:B7:5E:22:22",
            "root",
            "9WKA3KK3XN39",
            "9.3.13.44"
        ],
        "test2211": [
            "40:A6:B7:5E:33:11",
            "40:A6:B7:5E:33:22",
            "root2211",
            "221122112211",
            "9.3.13.82"
        ],
        "test2244": [
            "40:A6:B7:5E:22:45",
            "40:A6:B7:5E:22:46"
        ]
    }
}

If you want the final result to consist of only the keys common to both dictionaries it gets a little trickier, but this seems to work:

- hosts: localhost
  gather_facts: false
  tasks:
    - set_fact:
        dict3: "{{ dict3|combine({item: dict1[item] + dict2[item]}) }}"
      when: item in dict2
      loop: "{{ dict1.keys() }}"
      vars:
        dict3: {}

    - debug:
        var: dict3

Which produces:

TASK [debug] *******************************************************************
ok: [localhost] => {
    "dict3": {
        "poc-cu2": [
            "40:A6:B7:5E:22:11",
            "40:A6:B7:5E:22:22",
            "root",
            "9WKA3KK3XN39",
            "9.3.13.44"
        ],
        "test2211": [
            "40:A6:B7:5E:33:11",
            "40:A6:B7:5E:33:22",
            "root2211",
            "221122112211",
            "9.3.13.82"
        ]
    }
}

The above works by iterating over the keys in dict1, and for each key from dict1 that also exists in dict2, we synthesize a new dictionary containing the corresponding values from both dict1 and dict2 and then merge it into our final dictionary using the combine filter.

There are more options.

• Iterate the lists if list1 is properly sorted and provides exactly what you need

    - set_fact:
        result: "{{ result|d([]) + _item }}"
      with_together:
        - "{{ list1.0 }}"
        - "{{ list2.0|groupby('device')|map(attribute=1)|list }}"
      vars:
        _item: "{{ [item.0]|product(item[1:])|map('combine')|list }}"

gives the desired result

result:
  - device: LTM1_Device
    host: /Common/LTM1_Host1
    ip: 0.0.0.1
    link: LTM1_Link
    ltm_pool: LTM1_Pool
    port: '5555'
  - device: LTM1_Device
    host: /Common/LTM1_Host2
    ip: 0.0.0.2
    link: LTM1_Link
    ltm_pool: LTM1_Pool
    port: '5555'
  - device: LTM2_Device
    host: /Common/LTM2_Host1
    ip: 0.0.0.3
    link: LTM2_Link
    ltm_pool: LTM2_Pool
    port: '5555'
  - device: LTM2_Device
    host: /Common/LTM2_Host2
    ip: 0.0.0.4
    link: LTM2_Link
    ltm_pool: LTM2_Pool
    port: '5555'
  - device: LTM3_Device
    host: /Common/LTM3_Host1
    ip: 0.0.0.5
    link: LTM3_Link
    ltm_pool: LTM3_Pool
    port: '5555'
  - device: LTM3_Device
    host: /Common/LTM3_Host2
    ip: 0.0.0.6
    link: LTM3_Link
    ltm_pool: LTM3_Pool
    port: '5555'

(details)

• The next option is converting list1 to dictionaries

links: "{{ list1.0|items2dict(key_name='device', value_name='link') }}"
pools: "{{ list1.0|items2dict(key_name='device', value_name='ltm_pool') }}"

give

links:
  LTM1_Device: LTM1_Link
  LTM2_Device: LTM2_Link
  LTM3_Device: LTM3_Link
pools:
  LTM1_Device: LTM1_Pool
  LTM2_Device: LTM2_Pool
  LTM3_Device: LTM3_Pool

Iterate list2 and combine the dictionaries. The task below gives also the desired result

    - set_fact:
        result: "{{ result|d([]) + [_item] }}"
      loop: "{{ list2.0 }}"
      vars:
        _item: "{{ item|combine({'link': links[item.device]})|
                        combine({'ltm_pool': pools[item.device]}) }}"

(details)

- hosts: localhost
  vars:
    list1:
      - - device: LTM1_Device
          link: LTM1_Link
          ltm_pool: LTM1_Pool
        - device: LTM2_Device
          link: LTM2_Link
          ltm_pool: LTM2_Pool
        - device: LTM3_Device
          link: LTM3_Link
          ltm_pool: LTM3_Pool
    list2:
      - - device: LTM1_Device
          host: /Common/LTM1_Host1
          ip: 0.0.0.1
          port: '5555'
        - device: LTM1_Device
          host: /Common/LTM1_Host2
          ip: 0.0.0.2
          port: '5555'
        - device: LTM2_Device
          host: /Common/LTM2_Host1
          ip: 0.0.0.3
          port: '5555'
        - device: LTM2_Device
          host: /Common/LTM2_Host2
          ip: 0.0.0.4
          port: '5555'
        - device: LTM3_Device
          host: /Common/LTM3_Host1
          ip: 0.0.0.5
          port: '5555'
        - device: LTM3_Device
          host: /Common/LTM3_Host2
          ip: 0.0.0.6
          port: '5555'
    links: "{{ list1.0|items2dict(key_name='device', value_name='link') }}"
    pools: "{{ list1.0|items2dict(key_name='device', value_name='ltm_pool') }}"
  tasks:
    - set_fact:
        result: "{{ result|d([]) + [_item] }}"
      loop: "{{ list2.0 }}"
      vars:
        _item: "{{ item|combine({'link': links[item.device]})|
                        combine({'ltm_pool': pools[item.device]}) }}"
    - debug:
        var: result

ip: "{{ list2.0|map(attribute='ip')|list }}"
device: "{{ list2.0|map(attribute='device')|list }}"

ip: [0.0.0.1, 0.0.0.2, 0.0.0.3, 0.0.0.4, 0.0.0.5, 0.0.0.6]
device: [LTM1_Device, LTM1_Device, LTM2_Device, LTM2_Device, LTM3_Device, LTM3_Device]

link: "{{ device|map('extract', links)|list }}"
pool: "{{ device|map('extract', pools)|list }}"

link: [LTM1_Link, LTM1_Link, LTM2_Link, LTM2_Link, LTM3_Link, LTM3_Link]
pool: [LTM1_Pool, LTM1_Pool, LTM2_Pool, LTM2_Pool, LTM3_Pool, LTM3_Pool]

link_dict: "{{ dict(ip|zip(link)) }}"
pool_dict: "{{ dict(ip|zip(pool)) }}"

link_dict:
  0.0.0.1: LTM1_Link
  0.0.0.2: LTM1_Link
  0.0.0.3: LTM2_Link
  0.0.0.4: LTM2_Link
  0.0.0.5: LTM3_Link
  0.0.0.6: LTM3_Link
pool_dict:
  0.0.0.1: LTM1_Pool
  0.0.0.2: LTM1_Pool
  0.0.0.3: LTM2_Pool
  0.0.0.4: LTM2_Pool
  0.0.0.5: LTM3_Pool
  0.0.0.6: LTM3_Pool

link_list: "{{ link_dict|dict2items(key_name='ip', value_name='link') }}"
pool_list: "{{ pool_dict|dict2items(key_name='ip', value_name='ltm_pool') }}"

link_list:
  - {ip: 0.0.0.1, link: LTM1_Link}
  - {ip: 0.0.0.2, link: LTM1_Link}
  - {ip: 0.0.0.3, link: LTM2_Link}
  - {ip: 0.0.0.4, link: LTM2_Link}
  - {ip: 0.0.0.5, link: LTM3_Link}
  - {ip: 0.0.0.6, link: LTM3_Link}
pool_list:
  - {ip: 0.0.0.1, ltm_pool: LTM1_Pool}
  - {ip: 0.0.0.2, ltm_pool: LTM1_Pool}
  - {ip: 0.0.0.3, ltm_pool: LTM2_Pool}
  - {ip: 0.0.0.4, ltm_pool: LTM2_Pool}
  - {ip: 0.0.0.5, ltm_pool: LTM3_Pool}
  - {ip: 0.0.0.6, ltm_pool: LTM3_Pool}

result: "{{ [list2.0, link_list, pool_list]|community.general.lists_mergeby('ip') }}"

- hosts: localhost
  vars:
    list1:
      - - device: LTM1_Device
          link: LTM1_Link
          ltm_pool: LTM1_Pool
        - device: LTM2_Device
          link: LTM2_Link
          ltm_pool: LTM2_Pool
        - device: LTM3_Device
          link: LTM3_Link
          ltm_pool: LTM3_Pool
    list2:
      - - device: LTM1_Device
          host: /Common/LTM1_Host1
          ip: 0.0.0.1
          port: '5555'
        - device: LTM1_Device
          host: /Common/LTM1_Host2
          ip: 0.0.0.2
          port: '5555'
        - device: LTM2_Device
          host: /Common/LTM2_Host1
          ip: 0.0.0.3
          port: '5555'
        - device: LTM2_Device
          host: /Common/LTM2_Host2
          ip: 0.0.0.4
          port: '5555'
        - device: LTM3_Device
          host: /Common/LTM3_Host1
          ip: 0.0.0.5
          port: '5555'
        - device: LTM3_Device
          host: /Common/LTM3_Host2
          ip: 0.0.0.6
          port: '5555'
    links: "{{ list1.0|items2dict(key_name='device', value_name='link') }}"
    pools: "{{ list1.0|items2dict(key_name='device', value_name='ltm_pool') }}"
    ip: "{{ list2.0|map(attribute='ip')|list }}"
    device: "{{ list2.0|map(attribute='device')|list }}"
    link: "{{ device|map('extract', links)|list }}"
    pool: "{{ device|map('extract', pools)|list }}"
    link_dict: "{{ dict(ip|zip(link)) }}"
    pool_dict: "{{ dict(ip|zip(pool)) }}"
    link_list: "{{ link_dict|dict2items(key_name='ip', value_name='link') }}"
    pool_list: "{{ pool_dict|dict2items(key_name='ip', value_name='ltm_pool') }}"
    result: "{{ [list2.0, link_list, pool_list]|community.general.lists_mergeby('ip') }}"
  tasks:
    - debug:
        var: result

result: "{{ list2.0|zip(link_list)|zip(pool_list)|map('flatten')|map('combine')|list }}"

If you really want to append to content, you will need to use the set_fact module. But if you just want to use the merged lists it is as easy as this:

{{ list1 + list2 }}

With set_fact it would look like this:

- set_fact:
    list_merged: "{{ list1 + list2 }}"

NOTE: If you need to do additional operations on the concatenated lists be sure to group them like so:

- set_fact:
    list_merged: "{{ (list1 + list2) | ... }}"

I asked about lists vs dictionaries in the comment because of the impact it will have on the solution. If you were to restructure your data like this:

dict1:
  alice: ['role1', 'role2']
  bob: ['role1']

dict2:
  alice: ['role3']
  charlie: ['role2']

Then your solution becomes:

- set_fact:
    dict3: >-
      {{
      dict3|default([])|combine({
      item: (dict1[item]|default([]) + dict2[item]|default([]))|unique
      })
      }}
  loop: "{{ (dict1.keys()|list + dict2.keys()|list)|unique }}"

- debug:
    var: dict3

Which outputs:

TASK [debug] **********************************************************************************************************************************************************************************
ok: [localhost] => {
    "dict3": {
        "alice": [
            "role1", 
            "role2", 
            "role3"
        ], 
        "bob": [
            "role1"
        ], 
        "charlie": [
            "role2"
        ]
    }
}

If you're stuck with using lists, we can improve upon the json_query solution that Zeitounator suggested:

- set_fact:
    list3: >-
      {{
      list3|default([]) + [{
      'name': item,
      'roles': (list1|json_query('[?name==`' + item + '`].roles[]') + list2|json_query('[?name==`' + item + '`].roles[]'))|unique
      }]
      }}
  loop: "{{ (list1|json_query('[].name') + list2|json_query('[].name'))|unique }}"

- debug:
    var: list3

This produces your desired output:

TASK [debug] **********************************************************************************************************************************************************************************
ok: [localhost] => {
    "list3": [
        {
            "name": "alice", 
            "roles": [
                "role1", 
                "role2", 
                "role3"
            ]
        }, 
        {
            "name": "bob", 
            "roles": [
                "role1"
            ]
        }, 
        {
            "name": "charlie", 
            "roles": [
                "role2"
            ]
        }
    ]
}

Q: Is it possible to combine these two lists by the name key?

A: Yes. It is possible with the filter selectattr. The tasks below

- set_fact:
    new_list: "{{ new_list|default([]) +
                  [ item|
                    combine(titi|selectattr('name', 'match', item.name)|
                    list) ] }}"
  loop: "{{ toto }}"
- debug:
    var: new_list

give

"new_list": [
    {
        "ack": true, 
        "name": "titi"
    }, 
    {
        "name": "tata"
    }
]