At a pure level, Lambda "integration" is essentially an interface for passing in runtime arguments+environment to your application. If you're concerned about lock-in, you can write or integrate another entry point that executes your function on on-prem Tomcat or whatever other environment (Cloud Functions?) you want to run in.

The much harder challenge would be provisioning thousands of on-prem servers to handle the load, but I wouldn't necessarily qualify a dependency on cloud-like autoscaling as lock-in.

I guess the lock-in might come as you unwittingly couple yourself to the intricacies of the rest of AWS's offerings as your app architecture grows more complex.