Something very similar to this was already possible via serverless-express for node:

https://github.com/CodeGenieApp/serverless-express

This wraps Lambda's 'handler' function and allows express to run on top of it, essentially you get a node web server with no persistence between requests which usually isn't a good thing to rely on, but you can also kinda have that with persistent tcp connections.

Of course since this is not real HTTP, things like WebSocket aren't available, but it's good enough to build a CRUD backend or two.

Similar libs exist for other runtimes as well.