The only one of the three you mentioned that caused me hair loss was Lithium. It seemed like a lot, but I have always had such a huge mop of hair that I had no major visible signs of hair loss to others. The bathroom floor and tub were full of hair, though. Much more than prior to the hair loss. Also, my pony tails were much less thick than before.

My luck was that eventually (after maybe a year or so), the hair loss lessened, even while still taking Lithium at the same dose of 900 mg per day. I did eventually go off of Lithium a while later. My hair is quite thick again. I never lost hair from my eyebrows or lashes. I wish I had lost hair from my legs instead, but life can't be fair all of the time.

I took a dose of (1200 mg ?) Depakote ER for maybe a year and a half about 8+ years ago. I, personally, didn't have hair loss from that med. I've taken 40 mg Propranolol per day for about 12-14 years and no problems with that, either, or any other med.

Some supplements are supposedly good for Lithium hair loss, like Biotin, Zinc, and some others. I tried them and they weren't particularly helpful, but perhaps could be. I'd talk about supplements with your psychiatrist before taking any. See the article at Hair Loss as a Bipolar Medication Side Effect