I see your point, but this definition is so lax that it applies almost perfectly to any application I've ever deployed to the cloud. Using external services to save state isn't unique to lambda, any app hosted on a normal ec2 instance needs to follow the same pattern because the instance and its filesystem can go away at any time (unless you attach a volume, but I've always considered that to be bad practice).
Sure, it's a common pattern and the right one in many scenarios. But especially for non-cloud deployments it's very common to store session data in process memory or temp data to local disk, etc.
