The lich is the wise old man gone tyrant.
The lich, in life, could not stop for death so he became death.
The lich is immortality gone wrong.
The lich can also turn into a one-dimensional geriatic Skeletor joke if not played right.
My problem with liches is that they're often depicted as cardboard cut-out villains. Yes, they are terrifying to face, but DMs should give a lich different motivations besides accumulate more power. Sure, all lichs want more power, but we're talking about a creature that has the potential to "live" forever. Give them other goals.
For example: In Middle-Earth, the Witch King of Angmar's original purpose was to erradicate the Dunedain kingdoms in the North. It took "only" 500 years.
Also, who says liches have to look like withered corpses and skeletons? Maybe they look human, but if you cut them they do not bleed. You'd think with their command of magicks they'd know how to conceal themselves. In Ravenloft, Azalin, the ruler of Darkon, is able to do this.
One of the best supplement out there is the old AD&D 2e Van Richten's Guide to the Lich. This tome has lots of great idea to "flesh out" a lich, from his lair to his motivations. I hope WotC publishes the pdf soon.