What exactly are you trying to do here? Afaik Lambda isn’t meant to be used as a web server like Phoenix does. Maybe if you put it behind a load balancer or something you could get the requests from the lamdba entrypoint and forward them to Phoenix but that sounds a lot like bending a tool to do something it’s not meant to.
I’m still not sure what this has to do with Phoenix. Does your old project use it and you’re trying to shove it as-is in Lambda? Phoenix is at the same level of abstraction as Lambda: they’re both entrypoints to your application. Ideally your buisness logic is separate from that so it should be easy to ditch Phoenix and use Lambda’s entrypoint on its own.