If you're going to put everything in a single lambda function that's continually serving HTTP requests, you might as well look at ECS.
Source: I've rand both a Lambda Monolith and ECS on production and would pick Lambda any day
My bills are around $0.02 a month from API Gateway =)
AWS Lambda NEVER goes down. And if it does, it's most likely someone messing with DNS or backbone routing again and half the world is broken anyway.
It does need skill though, the billing model isn't as clear as "you pay me X euros a month for a server, I don't care what you do with it", but it's not dark magic either.
yes we have some very spiky workloads and we got bitten by that, subsequently we moved away from ECS for this exact reason