Beyond rules, the reason(s) why a lich seeks redemption might be argued.
So, what is a lich (as for D&D 3.5):
A lich is an undead spellcaster, usually a wizard or sorcerer but sometimes a cleric or other spellcaster, who has used its magical powers to unnaturally extend its life
According to D&D 3.5, a lich either can be arcane or divine.
Who wants to be a lich:
A cleric who devoted his life for his deity and his cause. If it was an evil deity and becoming a lich might be a purpose for him (any follower of Chemosh, the god of undead might be an example of this). In that scenario, redemption could not be a choice at all.
For a cleric of non-evil alignment, the character probably will commit great sins for his deity and his religion while becoming a lich. In that point, the character might need an atonement with a great quest to accomplish for his deity. That must not be easy as it sounds.
For arcane casters, situation gets complicated, since lich looks like a way to extend lifespan and get some extra abilities and powers, unless the character is heading for demilich. So, process and reason to become a lich is a way for greater power and life span.
A character dedicated his life for power and his magic and do not care the rest becomes evil (unless he is already evil) with thirst of power and domination and walks the paths of becoming a lich. He already knows the cost and makes himself ready for all! After becoming a lich and gaining a great lifespan and greater powers, it was hard to give away all these and quit the chance of gaining much greater power (becoming a demilich).
The way back?
So, according to that point, a character who becomes a lich probably will not seek redemption. If he does, then he must have good reasons for that.
In the situation of a previously non-evil cleric who became a lich, a great quest must be asked for his redemption, the reward (a restful death or a total redemption) might change according to deity and the quest accomplished, but that must be far beyond than taking another template.
In the situation for a arcane caster, I do not see any reason to turn back, especially after all those efforts and all these gains, adding the possibility for gaining greater power, an arcane caster would not turn back. But if he really wish for another chance, then I said NO! You must not started to walk in the dark path of becoming a lich and it is too late to turn back.
Well, in fact, it is a strict answer, I know. and I realize it is not complete.
In my games, role-playing is important and becoming a lich is not simply spending some gold, creating a phylactery and taking a template. Player must role-play and prove me that he really wants to become a lich. And my answer is what he will hear during that process. Also when he want to turn back, he will keep hearing that.
But in fact, it is all about role-play and if he keeps trying to find a way, then he might find a way. He must convince the gods (or the great power that can help him) in the process, so he must convince me for that. And it all about what he did and what sacrifices he accepted and what sins he commit.
If he finds a way to make amends for all he had done, then he will be redeemed.
But again, as a DM, do not tell this to your players or how they could redeem themselves. It must be something they must find out.