Lithium crystal circuits were part of the power generation system of Starfleet vessels in the 23rd century.
Over-expenditures of power could damage the vital lithium crystals at the hearts of these circuits, as happened to the Starship Enterprise in 2266, when chasing a Class-J starship into an asteroid belt. Forced to extend her shields around the vessel to protect it from asteroid collisions, the Enterprise burned out three of four lithium crystals, forcing the crew to supplement with battery power. The fourth crystal subsequently failed, overstressed from handling all of the ship's power. (TOS: "Mudd's Women")
The relation of a lithium crystal to a dilithium crystal has never been explained. It is possible its use was replaced by dilithium, or it could have been a related component.