The Lich King is a chosen champion of Imbross. The Lich King obviously has to be a Lich. Each Lich King wears the Helm of Dominion.
There always is a Lich King. The Lich King can't step down, and can only 'retire' by being killed. The killer instantly becomes the new Lich King. If said person is not a Lich yet, he will become one without the necessary ritual.
There are four Ancients bound to the Lick King, Garm, Grodd, Kirit, and Tengu. When a new Lich King or Queen is chosen, they instantly transfer ownership from the Dark Riders of the old Lich King to those of the new Lich King. If the new one doesn't have any/all Dark Riders yet, the weapons teleport to the Throne of the Lich and levitate there until a Dark Rider is made.
Previous Lich Kings include: Thargun Steelmountain, Arathor, Nerdril Deathcrown (current)
See: Order of the Liches