I've used SQLite over NFS for replication. It worked fine.
Though again, if you want true streamed (i.e. per query) replication, features like hot standby, etc... that's not part of the model and you're better served by a server-model RDBMS.
https://www.sqlite.org/backup.html
The way I've used it (for a db of 300-400mb loaded in-memory in a 64-bit app) was to load the .db in memory, then detect if there are changes outside (notified, or updated the .db file timestamp from a different app using the db), then load a second copy of the .db and compare, then build diffs and report them in some kind of API fashion.
It was used for live update of various level editing data for a game level editor. Possibly not the best fit (too much hierarchical data), but worked nonetheless.
One thing that I miss dearly from SQLite is some form of postgres arrays, but I'm so glad that recursive with has been added recently to SQLite which allows for hierarchical data (child/parent storing ids to each other) to fetch without some extra information.