Does lithium cause goiter?

It can. Lithium use is most commonly associated with a thyroid goiter with normal thyroid hormone levels. More rarely, hyperthyroidism may occur.
Yes, it can. Yes, lithium can cause goiter. Prevalence of this is about 20% in patients living in areas with enough iodine in the soil, to 87% in iodine-deficient areas or who are on long-term lithium therapy. Goiter can develop within weeks of starting lithium, but more often it takes months or several years. A smaller percentage of this group actually becomes hypothyroid. In most cases it's subclinical.