In case you don't know, my son is on the autism spectrum. He was misdiagnosed. Being on the spectrum, he used to do a lot of annoying little stims such as tapping his feet and hands on the school desks and not being able to sit still, while he pulled at his clothes--all common Autism Spectrum Disorders (ASD) behavior. On the Lithibod, he didn't do it as much because he was too sleepy. He didn't learn much in school either. It probably seemed like the mood stabilizer was doing it's job because he didn't seem as hyper. It wasn't until we weaned him off that we saw how much it was both doping him up and cognitively dulling him. You're Mom and if you don't think it's helping him, look for other opinions.
One other side effect my son had was that on the Lithium he peed in his bed every single night. About two days after his discontinuing it, he stopped and never did again.
Lithium is great and a lifesaver for some, but, if it is, the side effects still go along with it. I'm in a Bipolar Support Group. One common topic amongst us is the cognitive dulling and memory problems we all seem to have, from young to old (we have teens in our group). It's partly the disorder and partly the medications. I don't take a mood stabilizer because I can do without them and I don't like them--I've tried three and don't like how they made me feel. But many who have Bipolar I have absolutely no choice and for them mood stabilizers can allow them to be functional. The dosing is tricky with Lithium. You need to be sure it's not too low or not too high and the "good" dosage is very individual for each person. And if it's too low it won't work and if it's too high...it can be dangerous. You need frequent medication levels taken. My idiot psychiatrist never drew levels on me and I got toxic and very, very, very sick and suicidal...yes, on lithium. Also, thyroid problems are common (I had them on the Lithium). You weight the costs and benefits with a child because they can't tell you if they really feel better or worse.
When Lithium works, it's magic.