Nice, you can actually do something a bit more flexible using SQLite on AWS Lambda. "Just" mount an elastic file system (EFS) onto your functions. I wrote about it here: https://franz.hamburg/writing/shared-storage-for-lambda-func...
We've been building an experimental shared file system that specifically targets the FaaS setting. It supports SQLite and gets big performance gains over NFS/EFS, especially on read-mostly workloads, due to improved local caching and lock elision. See: https://arxiv.org/abs/2009.09845
How do you deal with ephemeral file storage? I guess you actually need the provider (say AWS) to build this into the platform?