I finally figured it all out. I know who the Lich is. First some history.
Lichs are necromancers who have gained eternal death by use of a mystical item known as a phylactery. This is an item or being in which Lich places his soul so that in the event his body is destroyed, he simply has to wait for it to be put back together.
Marceline's Dad said that Gunter's soul was the darkest he had ever seen. On the episode drawing by Muto and Suger, Ice King is seen helping the Lich despite not ever meeting him or truly being evil enough for the Lich.
The Lich King's phylactery isGunter