I'm not sure, I would say ask your doctor what you should do. Maybe just spread your water drinking throughout the day just to be safe until you can talk to him/her. I think the amount you have to drink highly depends on the dose you're on.
Lithium DEFINITELY causes stomach pains, but they're usually only while you're adjusting to a dosage change. When I change mine, I feel really sick and nauseated and my stomach hurts, and then it dies down in a few days.
My shrink didn't tell me I had to drink water at certain times, but then I'm only on 750mg. I just drink when I'm thirsty (which is most of the time, thanks to the lithium). My shrink reckons that's good enough.