SPOCK: The entire ship's power is feeding through one lithium crystal.
KIRK: Well, switch to by-pass circuits.
The Alternate Factor showed dilithium crystals, they looked very different than the one lithium crystal seen in Mudd's Women.
It sounds like using the crystals is an option in the TOS era. Possibly they give an advantage, but aren't strickly speaking required. The TNG era would seem to need them to operate at all.