Well, I have had tremors on lithium within a normal blood level, but sometimes my levels have gotten too high and the tremors were much more noticeable. I was toxic once, and it felt almost as if I was drunk, I was very confused, I couldn't walk in a straight line, and I overall felt very sick, very nauseated, and slurring my speech very badly. My friend noticed it right away and got me to the hospital.

The tremors are yes a side effect. However they can also be a sign of toxicity, if you look it up it is listed as a symptom of toxicity, except that you may notice that sometimes it will be defined as coarse trembling of hands and legs, instead of fine tremors.