It's very important to use the right terminology here. People are not taking lithium (a reactive metal) ,they are taking lithium salts,primarily lithium carbonate (LiCO3).
It's clear that in any normal diet, lithium salts are going to be present in trace amounts.
In light of this,It's important to have properly designed experiments to determine whether there is a basal role for Li+ ion in normal human physiology; this should be done using several different lithium salts (LiCO3,LiCl, Lithium acetate, lithium nitrate,lithium citrate) ,to determine whether the role of the anion involved,is equally vital to observed results.