Due to the “longish” running nature of the two sync processes that I moved to lambda (both take around 10–15 seconds to complete) I have not really paid attention to response time. I did some initial hello world tests just returning hardcoded json and there the response was around 200ms +-which would be perfectly fine with me. I have read about the warm up issues, if you have enough traffic it should not be an issue as AWS keeps the instance running your lambda function around for a while making subsequent requests fast. Maybe if you combine it with the new cron scheduling feature you could keep it “awake” getting rid of that issue all together.
The datastore behind my project is NoSQL (parse.com) which does not have full text search. I am working on adding search with AWS elastic search (just announced) and lambda, and there response time will be an issue. I am happy to share my findings once I have it running.