We use Lambda + API GW to manage the glue between our different data/service providers. So for instance we expose a "services" API (API GW) that takes a request, does some business logic (lambda code), calls the relevant provider(s) and returns the aggregate response.
That principle can (and probably will) be extended to hosting our own back-end / business logic.
We're trying to get to the point where a dev only needs to write a Swagger file, the lambda code and a bit of configuration, and the rest is taken care of by AWS and our CI framework.
Do you worry about vendor lock in, which is coming up a lot on this comment section?