Recently we built a prototype for the replacement of a simple HTTP service with API Gateway and Lambda instead of classic nginx and WSGI apps on EC2.

It is very promising technology (even if I'm not totally buying into the serverless idea yet) but the cost of API Gateway considering a significant load on the service was prohibitive. I would really like someone to prove us wrong and see if we missed something in our analysis. Until then, I find that this is usable only for relatively low traffic services.