I've had really bad experiences trying to serve web workloads from lambda or cloud functions type services. The ramp up period to scale for a sudden influx of traffic is ridiculously slow. basically it can't handle a thundering herd at all unless you pre-provision enough concurrency which is incredibly expensive.
I'm sure these kinds of services have good use cases for back office async tasks and things like that, but for web workloads it doesn't really work.