With Lambda you pay per 100ms / per-1-million-requests. So, yes, it's very proprietary at the moment, but for any service that sits idle most of the time it can be very cheap.

https://aws.amazon.com/lambda/pricing/

If you were hosting something like a little message board for your friends and family, or something you are demoing to to possible employers, etc, it'd be borderline free, but available all the time.