Warm Lambdas (using Zappa's auto keep-warm) are actually 20-40ms, which makes them suitable for web servers.
While this probably keeps the majority of the requests warm, I would expect that there would still be some cold ones every now and then. Amazon doesn't provide a guarantee in how the containers get recycled.
This is just me speculating, though.
[1] - https://www.iopipe.com/2016/09/understanding-aws-lambda-cold...