|The following information is from the Adventure Time comic book series.|
It may not be part of the same canon or continuity as the animated series.
The Echo of the Lich is a wraith of the Lich made by the Lich in case he was ever defeated.
When Ice King and Hunson Abadeer were making their dungeon, the Lich appeared and knocked them both out for three weeks, while he built his own part of the dungeon, Lich Land. In it he put a part of himself in the dungeon that would be unleashed upon entering Lich Land.
Years later, Finn, Jake and the Ice King came to Lich Land hoping to destroy whatever's left of the Lich. Upon entering the dungeon, the Echo invaded their minds putting each of them in fantasy made from their memories, hoping to put them somewhere they wouldn't want to leave while it summoned enough minions to kill them and then invade Ooo. It put Finn in Farmworld with his mom and Farmworld Jake, Jake in a world where Finn has stretchy powers and BMO and Princess Bubblegum threw him a picnic and put Ice King in a dungeon where Betty was being held.
After being able to escape the illusions, they confront the Echo, who insults the trio but takes special aim at Ice King who it belittles as a senile old man with no loved ones and will die alone. Ice King ignores these insults and distracts him long enough for Finn to put Jake in it's skull and grows so big it shatters it.
The Echo of the Lich is a wraith of the Lich, but has somewhat different abilities. For example, the Echo does not seem to have the ability to take control over a person's mind, but instead he has the ability to look into a person mind and create an illusionary world that appeals to that person. The only way to get out of the illusion is to show love, which the Lich finds so repulsive that the illusion will cast the person out of itself. On the other hand, if the person does not wish to leave the illusion or the illusion self is about love, the only way to get out is to make that person face reality and the illusion will shatter.