We do this at current job for most of our internal tools. Not a setup I would choose on my own, but serviceable. Using a simple handler function that uses mangum [0] to translate the event into a request compatible with FastAPI, it mostly Just Works TM the same in AWS as it does locally. The trade off comes with a bit harder troubleshooting and there are some cases where it can be difficult to reproduce a bug locally because of the different server architectures.
0: https://github.com/Kludex/mangum