Redis without some clustering is going to be a SPOF, I’d definitely check out PubNub/Pusher and friends, they’re pretty cost effective and save the hassle there, at least until you “out grow” those.
FWIW you can deploy existing Express (or any other Node app) to Lambda with a technique like https://github.com/apex/up uses, launching a server inside the Lambda with no real drawbacks in terms of performance etc.
Why is startup always the default these days? What turns people away from just building real companies? It’s more difficult in some ways, but it’s also more rewarding, and you have of course more freedoms and fewer mouths to feed. It forces you to fix all of these problems from the get-go, because you will fail very quickly otherwise haha.