I use the AWS Toolkit for PyCharm; it automates most of the process, including pulling an image (built by Amazon, I believe) that emulates the Lambda environment. All I have to do is write the Lambda function with the correct method signature, designate it as such, start a debug session, and PyCharm + Docker do the rest. It's insane that PyCharm Professional only costs $100 or so, it saves me that much in development time in a single day.

Edit: all of the above will work with the free version of PyCharm, I believe, but without the in-IDE control panel for Docker (which you don't absolutely need).