I was testing the MediaWiki-Debian package (though I believe it's applicable to vanilla MediaWiki) and discovered that VE/Parsoid isn't working on SQLite. Read requests seem to work, in that I'm able to open the editor, change stuff, but when I try to save, I get Error contacting the Parsoid/RESTBase server: (curl error: 28) Timeout was reached.
My hunch is that the loopback is causing a problem in that the first API action=visualeditoredit request holds some lock on the database, and then the loopback request times out because it can't get the lock.
Everything works fine on MySQL.