Lambda via API gateway requires a lot of traffic to be fast. From what i've read, it's because of the SSL handshake between the Cloudfront POP (which all API Gateways use automatically) and Lambda. Only when you have a lot of traffic will enough SSL sessions be cached to get a good hit rate.
(I haven't tested this myself, just what I've gleaned from the forums.)
Yeah, I'm skeptical about that though, as I still see lowest requests in the 400ms range when hitting the API Gateway with serious load (say 100k requests running at a 400 req. concurrency level). Also, even if you cache SSL sessions you still have the cold start problem when your Lambda scales beyond the container it's initially running in if you have a large number of concurrent requests.
That said, I'm excited for the potential of serverless offerings - whether using containers or any other implementation mechanism. I'm building a backend for a native app right now and the initial beta version was using Lambda. The slow responses really made it tough though so a move to GKE and Kubernetes have made response times a lot lower, and it actually scales faster too.
