well, when you become a Lich all feelings die along with the body, you remember who you are and retain all memories from before but you have no feelings, no empathy or anything, you'll simply be a cold wandering skeleton that really doesnt care about anything but studiyng magic and becoming more powerful.
and besides that you pull your soul out from your body and place it in a jar or crystal or whatever you choosed as a soulholder.
i would guess that makes Liches True Neutral or something, since they would only kill you if you annoy them or they see you as a threat to their plans.
From the few we can interact with, I'd stay that most emotions go and leave only behind the purpose for which you became a lich - since the most common reason for becoming a lich is to have time for study and increase of magical power, they're the most common personality trait.
Revenge and ambitions are also quite common, duty is rarer. But there's one thing to consider : as a lich is technically immortal, most of them don't feel any need to hurry their plans - they'd rather spend yet another century to hone and polish them to perfection than take the slightest chance. With the pesky mortals that keeps
changing things around, it means constant tampering and adjustement - and further delay. That's why those plans seldom comes to fruition : there's alway some new development to take into account.