The best solution I've found for local testing is the Lambda Runtime Interface Emulator (RIE)[1]. It's basically a little Go wrapper[2] that runs your handler and makes it callable through an HTTP API. I considered writing a test harness around this for convenient integration testing but in my recent evaluation, I ended up avoiding Lambda (it's been really nice for small one-off tasks but was too expensive for the most recent and somewhat fringe use-case I considered using it for).
[1]: https://docs.aws.amazon.com/lambda/latest/dg/images-test.htm... [2]: https://github.com/aws/aws-lambda-runtime-interface-emulator