You may use a Map for this:

public static String manageFilters(Map<String, Object> lines){
    System.debug('### lines : ' + lines);
    System.debug('### lines.values() : ' + lines.values());

    for(String key : lines.keySet()){
        System.debug('### lines.get(key) : ' + lines.get(key));
        System.debug('### >>> ' + lines.get(key));
        Map<Object, Object> test = (Map<Object, Object>)lines.get(key);
        System.debug('### test ' + test);
        System.debug('### test ' + test.get('ObjectName'));
    }

    return null;
}

Map has a values() method that returns a List containing every value in the map.
If you have to check only one value, you could just call contains() on that list, while if you have to check multiple values you should create a new Set with those values then call contains() (or containsAll()).

Map<String, Integer> myMap = new Map<String, Integer>();
myMap.put('key1', 1);
myMap.put('key2', 2);
myMap.put('key3', 3);

List<Integer> mapValues = myMap.values();
System.debug(mapValues.contains(1)); // true

Set<Integer> mapValueSet = new Set<Integer>(mapValues);
System.debug(mapValueSet.contains(2)); // true
System.debug(mapValueSet.contains(5)); // false

Keep in mind that List.contains() runs in linear time (O(n)) while Set.contains() runs in constant time (O(1)).

Using account id as example is terrible idea because they'll be unique -> your lists would always have size 0. But yes, you should be able to do something like that.

Your stuff doesn't even compile, you can't use "=" in for(Account acc = [SELECT...]).

Let's say you have accounts and some of them have duplicate names. This would be close to what you need:

Map<string,List<Account>> accountMap = new Map<string,List<Account>>();
for(Account acc : [SELECT Name, Description FROM Account LIMIT 100]){
    if(accountMap.containsKey(acc.Name)){
        accountMap.get(acc.Name).add(acc);
    } else {
        accountMap.put(acc.Id, new List<Account>{acc});
    }
}

and then yes, if you'd have the key you can access accountMap.get('Acme Inc.')[0].Id

Replace

counts.put('month_total',counts.get['month_total']++);

with

counts.put('month_total',counts.get('month_total')++);