Being a big fan and supporter of the Lich unlifeform - my roots go way back to the Sandro Should Have Won Movement (or SSHWM) - I am biased in my opinion but have to say that I wholeheartedly agree.
Now, I don't necessarily think that starting out as a Lich should be possible, being a Lich is a very coveted position in unlife and shouldn't simply be handed out to players, they should have to work for it, preferably through a series of quests or through finding a rare artifact in one of the dark corners of the earth. Of course a companion of Undead origins could be a possibility too, as their views on life, the universe and everything always make for interesting dialogue and character interaction.
Naturally, becoming a Lich or other sentient undead in a world where souls are in constant reincarnation and forget their past lives, as well as (possibly) losing their past power would be irresistible, and it would be outright insane to not include such an option for a character.