There's now a "server-process edition" as well:
Basically, it allows simultaneous writers to the same database, provided they are all in the same process (SQLite is per-thread). All you'd have to do is add a wire protocol and you'd have a sqlite daemon. HTTP might be a good choice: POST your SQLite program to the daemon and get back the results. You'd probably want the results to be in ".headers on" and ".mode quote" format, as that is the most information-preserving.