As long as SQLite doesn't catastrophically break under load it's fine for production, but only as long as it has a single client; traditional database engines can deal with multiple applications connecting to them.

I'm using sqlite for a production application as well, but its load will be in the range of - at best - thousands per day. The only complexity will be that there has to be a secondary 'fallback' server; the current application just copies the whole .db file over to the secondary server after certain events.