please be careful in equating the two: there are decades of studies, including large trials, demonstrating benefit for lithium. It's considered gold standard treatment for bipolar disorder even in an era where big pharma pushes hard for newer and more costly meds.
there is modest and inconsistent evidence from small trials that chromium picolinate, a dietary supplement, may be beneficial in depression.
Oh, and note that chromium is more expensive than lithium too!
My personal experience (n == 1) study finds that a couple of Chromium GTF taken sublingually (ie sucked under the tongue) works instantly to improve my mood.
I never use picolinate.
Sublingual is so that it can cross the blood-brain barrier. I can use less Chromium that way to get the same improvement in mood.
My pet hypothesis is that it works by displacing Vanadium from the brain. Vanadium and Chromium are very similar chemically, and some studies suggest that Vanadium is elevated in manic-depressives. Particularly, I'm high in Vanadium because I live in Japan and eat a lot of whole fish and seaweed.
The main possible negative side-effect was that I needed more Manganese to balance the Chromium. That I worked out from developing mild dermatitis, that went away when I supplemented Manganese. [1]
None of the above is a recommendation - your mileage may vary etc. Everything you supplement has side-effects. Particularly, supplementing one bivalent metal can create a functional deficiency in another. In this case, I wanted to reduce the effects of Vanadium but I ended up reducing Manganese too. Anyway, people need to do their own research to see what works for them.
> big pharma pushes hard for newer and more costly meds.
Lithium is not perfect. It causes permanent kidney damage and is a pretty bad teratogen. Also overdose is pretty bad, which is never ideal for a mood medication.
There is actual value in investigating new medications for bipolar beyond big pharma profits.
(edit to add: re lithium: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5947163/; re chromium, I could find one RCT with n=15 in depression)