Is lithium L-threonate a potential brain medicine?
Lithium has a diagonal relathionship with magnesium, so in effect, it makes sense to compare it to magnesium compounds. It may also substitute for sodium ions in transporters. I doubt the counter ions is relevant, since most Li coumpounds are quantitatively dissociated. Stable concentrations of lithium are only achieved after several week of treatment. Lithium carbonate, citrate and sulfate are used to my knowledge. Plasma concentrations are monitored so as to avoid reaching toxic levels (more than 1 milli molar). Some physicians also test for the concentration inside red blood cells to get an idea of the concentration in the brain, but this has not been confirmed to be relevant. What is important is not the amount of it, but the clinical effect : is the patient responding to treatment ? does he/she support it ?

Lithium has not only neuroprotective effects, but also mood-stabilizing effects. It is mostly used in case of bipolar disorder (mood swings), but also as an antidepressant. The mechanism of action is still elusive. It may enhance serotonin pathway, and, by competing with magnesium ions, inhibit some magnesium-dependent enzymes (typically enzymes handling MgATP). One of these enzymes is called glycogen-synthase-kinase (GSK).