My understanding is that Lambdas aren't ever really truly warm unless you have a completely steady traffic level. The first request in a while will hit the latency spike. But so will every increase in concurrency. So if you were serving 2 req/sec, and a 3rd concurrent visitor comes along then they will also get a cold start.
If you have a low-latency use case then fly.io's regular VMs are much better than either this or lambda. You get permanently running VM (the smallest of which is $2/month for 256mb/RAM), which can serve more than one request all by itself and will auto-scale with traffic.