As an example, you'd write your entire API as a flask app, and then deploy that app to Lambda. Then send all requests to that one Lambda. As long as your startup time is quick (and your datastore is elsewhere, like in DynamoDB) then it will work great for quite a while. Lambda will basically run your app enough times to handle all the requests.

You have to be careful when you design it such that you don't rely on subsequent requests coming to the same machine, but you can also design it so that if they do come to the same machine it will work, using a tiered cache.