I am not sure about the frameworks, but a lambda function is just that, a function. You can easily run your function and pass in an event object (a dict in Python) to test various scenarios. You don't need to deploy to test. Once you are ready you can deploy to lambda without publishing to fully test before publishing live.
I am currently using it for what you could probably call a user interface. My use case is forms stored in S3 served as an iframe which POST via JS to AWS API Gateway that calls lambda to process the form and return the result to the user.
But if you want to emulate the aws gateway + lambda cycle locally it seems like you need a bit of rigging to do this easily, especially if you want to talk to it with your browser.