You can't gain weight without eating more. According to Why Does Lithium Cause Weight Gain? lithium binds to a receptor 5-HT1B which influences the serotonine system influencing your mood, and also your appetite. This is the 1999 paper by Olivier Massot they refer to 5-HT1B Receptors: A Novel Target for Lithium: Possible Involvement in Mood Disorders.