It's possible to run SQLite on an NFS share (with caveats: file locking must work correctly, WAL mode does not work at all). AWS EFS Elastic Filesystem specifically calls out its compatibility with SQLite. https://aws.amazon.com/about-aws/whats-new/2017/03/amazon-el...
I would definitely not try using this in a write heavy workload but could be interesting to consider in a write occasionally scenario.