Lambda containers serve multiple requests. You just write the code as if you were handling a single request. And on the contrary, Lambda latency is worst when you have spiky traffic patterns (such as for a seldom run function). Of course, if you can tolerate the cold start latency overhead, Lambda is also a cost effective solution for those seldom run functions.

Also, specifically for Aurora, Lambda supports transparent connection pooling. It is just no longer a concern of your application code.

Disclaimer: I work on serverless services at AWS. I’m definitely biased :)