I know that this is a nitpick, but I think that this should be usable with just:
python -m lambda_local

This is relevant for debugging where one might start this using the python command rather than from the entry point.

It's as simple as using a __main__ file that calls the same function as the __init__ file when its __name__ == '__main__'. Any configuration that may use python -m lambda_local.__init__ would not be affected.