Have you analyzed the pills for Lithium content? It's quite possible that it's more like the different brands have different amounts of Lithium in them - it's fully possible that some brands you got were fakes, and didn't contain enough mineral.
It's kind of impossible to answer this question btw - because the science is rather thin. I believe multiple studies have shown that most lithium-salts are very similar though, just that the dosing varies, because of varying bioavailability.
Btw, look into Lithium Salicylate, for the future - it's currently completely unavailable, but it could end up being the greatest of the lithium-salts, since the bioavailability is similar to LiO, but Salicylic Acid itself is also a powerful neuro-anti-inflammatory - thereby increasing efficacy in Bipolar depression even further. Look it up.
(oh, and start requesting nootropics-vendors to actually f***ing manufacture it...)