I guess you mean the API-Gates + Lambda. Not sure - I think thats something that should be handled by some separate tool (APIGatesgger? ;) - lets hope its not another dirty word)
Serverless is way much more advanced machinery than this tool.
My point was to create a tool, not a whole ecosystem around AWS Lambda.
When it comes to serverless - my main concern (as it was with Lambda without env variables), is with storing configuration data along the code in the repo. Additionally the reason for creating was mostly pipelines.
I didn't plan to do the push-to-deploy thing, mostly because that would totally complicate things. The rationale was more that we would use the CI that would automatically build and deploy things to DEV env that would be then promoted around.