Are the side effects of fluoride similar in a way to lithium?

In a word, No. The potential side effects of Fluoride and lithium are very different. The only similarity is that both must be ingested to cause side effects.
No. Moderatle amounts of excess systemic Fluoride ingested by young children while their permanent teeth are forming (birth to age 6) can cause flourosis. Most cases in the U.S. Are very mild. High, long term (several years) exposure to systemic Fluoride and cause skeletal fluorosis. Only 4 cases in the U.S. In past 30 years. Topical Fluoride has no adverse effects. Lithium is totally different.