Lamdas aren't stateless or ephemeral either. Anything that occurs on code load will persist on that container (i.e., if you initialize something at the module level in Node, it will persist between calls to the same container; this can cause all kinds of weirdness if you aren't aware of it. For instance, I have seen where a dev read some data at load time, and then performing destructive operations on it as part of data transformations in the code, and then wondered why he was getting non-deterministic results back). And there's a half gig of temp space on each container you can write to as well.

While the definition of what constitutes 'serverless' is pretty ambiguous, no one includes ephemeral state as a systems requirement, else you have something useless.

DynamoDB is generally viewed as serverless because there's no management of an underlying VM, and for some definitions because it can scale out horizontally automatically, without downtime, to meet demand (as compared with RDS, or another managed database solution that can only scale vertically).