One theory is that increased thirst leads people to drink high-calorie fluids. Other possibilities include endocrinological mechanisms leading to an increase in fat storage and lithium-induced hypothyroidism, which slows metabolism causing less burning dietary calories in general.
A 1999 study (see link below) showed that on a molecular level, a particular receptor known as 5-HT1B is a "target" for lithium (Massout et all, 1999). These receptors are known to be controllers of the system that distributes serotonin, an important neurotransmitter in the chemistry of depression - AND APPETITE. It is possible, then, that one mechanism by which lithium fights depression is related to the side effect of weight gain.
Patients taking lithium should be prepared to make lifestyle changes as necessary if this particular side effect appears - changes including reducing or eliminating caffeine intake, switching from sugary soft drinks to calorie-free water (flavored or plain), and increasing exercise. They should also be on the lookout for other side effects and the symptoms of lithium toxicity, to protect their future health.
Lithium remains one of the drugs of choice to treat bipolar disorder, with good reason. We have good reason to be thankful for John Cade's powers of observation.