You asked for real-world experience. Here's some:
SQLite locking is robust, ASSUMING the underlying (networked) file system is also robust. Historically, that's been a poor assumption. Recent operating systems get it much better.
If you play by the rules, your biggest problem will be cases where the database stays "locked" for many minutes at a stretch. For example, if the network drops an "unlock" request from a reader, you might be unable to write until the lock expires. If an "unlock" from a writer goes missing, you'll be unable to read. (To be fair, you can experience the same problems with ordinary documents.)
You'll get fewer problems on a good reliable network with "opportunistic locking" (client-level file caching) disabled for the database.
