Can I add a new local secondary index to an existing DynamoDB table?
no, you cannot do this, only adding a global secondary index is possible for an existing table.
from the documentation :
Local secondary indexes on a table are created when the table is created.
Read the documentation below. You can find the differences between GSI and LSI in the table.
https://docs.aws.amazon.com/amazondynamodb/latest/developerguide/SecondaryIndexes.html