One Lambda, two services?

It's certainly possible to register multiple triggers for a single lambda. We'd need to know the steps you're taking and the errors you're seeing to say more about what's going wrong in your case.

However, multiple triggers make things complicated, since you need to add logic for determining what kind of event you were invoked with, and then handle the different event formats before invoking the common code. It might be better to have two different lambdas to handle the different triggers. You might either include the common code in both deployment zips, or factor it into a layer.

I was thinking to have the same code acting as a REST service behind the API gateway, and also handle CloudWatch scheduled events. Thus there would be two entry points, no need to differentiate between inputs.

The errors I receive are from the Quarkus framework which won't support my idea, so I was curios whether it's a Lambda principle or a Quarkus limitation. I'll go anyway with two lambdas as you suggested but I'd like to understand the principle behind...