When supplementing with otc lithium orotate/aspartate, should blood tests still be done regularly to monitor lithium levels, same as prescription lithium types?

It depends: It depends on how much you're using. Usual doses of Lithium Carbonate for bipolar disorder are in the range of 900 mg - 2400mg/day acutely, and 400 mg-1200mg/day maintenance. At these levels, serum monitoring is needed to avoid toxicity. Lithium orotate is given in smaller (10-20 mg/day) doses -- and although much less likely to cause toxicity at that level, it still can in some.