When I was on Lithobid (a time release formulation of Lithium) I never had a drowsiness problem, but we are all different. In fact I had gone to that instead of Depakote, for that knocked me out so much, I even fell asleep driving, twice, so I asked pdoc for Lithium. My brother has been on Lithjium for ages and he was able to work with machinery,drive and lead a "normal" life.
Maybe it's just an adjustment period or some flu bug you caught. Take it up with the prescribing physician if this continues.
Meanwhile take care, hope you feel better soon, get lots of rest.