no, you cant do it, only adding global secondary index is possible to an existing table.

from documentation:

Local secondary indexes on a table are created when the table is created. 

You cannot create on an existing DynamoDB table, from the AWS documentation:

To create one or more local secondary indexes on a table, use the LocalSecondaryIndexes parameter of the CreateTable operation. Local secondary indexes on a table are created when the table is created. When you delete a table, any local secondary indexes on that table are also deleted.

You would need to either use a global secondary index, or migrate to a new table that you create the LSI at create time.

Edit (January 2015):

Yes, you can add a global secondary index to a DynamoDB table after its creation; see here, under "Global Secondary Indexes on the Fly".

Old Answer (no longer strictly correct):

No, the hash key, range key, and indexes of the table cannot be modified after the table has been created. You can easily add elements that are not hash keys, range keys, or indexed elements after table creation, though.

From the UpdateTable API docs:

You cannot add, modify or delete indexes using UpdateTable. Indexes can only be defined at table creation time.

To the extent possible, you should really try to anticipate current and future query requirements and design the table and indexes accordingly.

You could always migrate the data to a new table if need be.

Why is that?

Changes to LocalSecondaryIndexes require replacement of DynamoDB table, since LSI can only be created on the table create time. In contrast, modifications to GlobalSecondaryIndexes lead to no interruption.

Can that be prevented somehow or is there a Workaround besides adding the index manually via the aws-console?

Sadly, there is no way to prevent this, as explained above. You can use GSI if you don't want to keep replacing your tables.

You will need to use the GlobalSecondaryIndexUpdate way of doing this, as described here: https://docs.aws.amazon.com/amazondynamodb/latest/APIReference/API_GlobalSecondaryIndexUpdate.html

It should look something like this

CreateGlobalSecondaryIndexAction action = CreateGlobalSecondaryIndexAction
                .builder()
                .indexName("index-name")
                .keySchema(theSchema)
                .build();
GlobalSecondaryIndexUpdate index = GlobalSecondaryIndexUpdate
                .builder()
                .create(action)
                .build();
UpdateTableRequest request = UpdateTableRequest
                .builder()
                .tableName("table-name")
                .globalSecondaryIndexUpdates(index)
                .build();
dynamoDbClient.updateTable(request);