It's funny we tested lambda + Amazon gateway api this week at work.
It's awesome!.. Until you have to deal with the cold start issue. Our first call takes about 1.5 seconds; and then all other calls take about 50-80ms.
Your container stays in cache about 5-10 minutes unless it is called back, there are no guarantees.
This micro service is not called often and for us 1.5 seconds is never acceptable.