definitely, lithium is known for irritating stomachs and causing nausea. For me, it depends on how much i'm taking at once. I find that if i take 600mg at a time, the nausea is noticeable but mild and controllable. if i take 900mg at once though, i become nauseous enough to throw up. Doctors recommend that you take it with food or with milk, but neither of those work for me. Rather, that just means there's more coming up.
if the lithium serum levels in his blood are safe and steady, then the nausea probably is not a sign of lithium toxicity. Breaking up the doses into a morning and night regiment might help, or what I do is take it right before bed, and I end up sleeping through the worst of it.
Hope this helps!