The manipulative influence of Ice King’s crown, its magical powers, and the fact that it gives its wearer unpleasant visions make it reminiscent of “The One Ring” from J.R.R. Tolkien’s Lord of the Rings series. 

The Ice King and Gollum/Smeagol have similar traits from their artifacts: -Unnatural long life (Smeagol was an early hobbit type while Simon was a human.) -Loss of sanity  -Change in appearance

It is shown than the Ice King is uncomfortable sharing his crown..A good example would be in "What Have You Done" when Finn and Jake remove his crown while imprisoning him. Smeagol had a strong obsession and went bonkers after the ring was lost. (He bit off Frodo's hand for the ring, I mean, c'mon.)

The last thing I'd like to point out is that in the Season 4 finale, the enchiridion uses the jewels of power to make a portal..blah blah. On the enchiridion, the side had a form of Elvish writing on it. Pen Ward IS a fan of LOTR, so it is possible he would put that in as a reference. 

With the Lich wanting the Enchiridion (and the jewels needed to fuel it) for it's powers, would the Lich be able to be compared to Sauron, The Dark Lord?

(I wrote this on other sites too but I didn't get much feedback. I just want to hear ideas.)