Yes...depending

Alignment causes a lot of arguments around the D&D community. There are a pair of rock-solid methods: the Sanctify the Wicked spell, and the redemption rules, both of them found in the Book of Exalted Deeds. The BoED can be a controversial book in some groups, but those rules are a definite method of getting the lich back on the straight and narrow.

And then we get to the less-clear part.

D&D's alignment system can be inconsistent at times. Some sources say alignment is about action; other sources imply that it's about the intent behind an action. There's elements of belief systems and thought patterns in alignment too, which complicates the matter further. The Player's Handbook says alignment is supposed to be a guide; other sources treat it like a straightjacket. All of this makes the question, "Could this lich seek redemption on his own?" extremely difficult to answer.

I am inclined to say yes, no being is past redemption. The idea that any being with free will, down to the most vile and wretched demons, can find redemption is the cornerstone of how the Good alignment treats others. Celestials and fiends are polarized by these opposite beliefs - that any being is capable of redemption (even if it's not) in the case of celestials, and that no being is above corruption (even if it is) in the case of fiends. While an argument could theoretically be made that fiends are past redemption (an argument that's riddled with holes - there are canonical examples of non-evil fiends), the lich you're discussing is a mortal, born, living, and now undead with full control of their own free will. If they have a reason to turn from evil - even if that reason is weariness, or a craving for acceptance - then I don't see a reason that they can't, especially if it makes a good story.

As for true death, there's a few avenues for that - the easiest is for the lich to smash his phylactery, then kill himself. However, there is another option - regaining mortality. Resurrection and True Resurrection can both return an undead being to true life, and by RAW you don't even need to break the phylactery. The lich would be mortal once again, but would be able to live out the rest of their natural years and then die in peace.

As to the greater question of if their act of unspeakable evil to become a lich can be forgiven...in the spiritual sense, the Book of Exalted Deeds states that no being is beyond forgiveness if they truly seek to repent - at least, not in the eyes of the forces of planar Good and the gods of that alignment. Forgiveness from the lich's victims is another matter entirely.

Yes...depending

Alignment causes a lot of arguments around the D&D community. There are a pair of rock-solid methods: the Sanctify the Wicked spell, and the redemption rules, both of them found in the Book of Exalted Deeds. The BoED can be a controversial book in some groups, but those rules are a definite method of getting the lich back on the straight and narrow.

And then we get to the less-clear part.

D&D's alignment system can be inconsistent at times. Some sources say alignment is about action; other sources imply that it's about the intent behind an action. There's elements of belief systems and thought patterns in alignment too, which complicates the matter further. The Player's Handbook says alignment is supposed to be a guide; other sources treat it like a straightjacket. All of this makes the question, "Could this lich seek redemption on his own?" extremely difficult to answer.

I am inclined to say yes, no being is past redemption. The idea that any being with free will, down to the most vile and wretched demons, can find redemption is the cornerstone of how the Good alignment treats others. Celestials and fiends are polarized by these opposite beliefs - that any being is capable of redemption (even if it's not) in the case of celestials, and that no being is above corruption (even if it is) in the case of fiends. While an argument could theoretically be made that fiends are past redemption (an argument that's riddled with holes - there are canonical examples of non-evil fiends), the lich you're discussing is a mortal, born, living, and now undead with full control of their own free will. If they have a reason to turn from evil - even if that reason is weariness, or a craving for acceptance - then I don't see a reason that they can't, especially if it makes a good story.

As for true death, there's a few avenues for that - the easiest is for the lich to smash his phylactery, then kill himself. However, there is another option - regaining mortality. Resurrection and True Resurrection can both return an undead being to true life, and by RAW you don't even need to break the phylactery. The lich would be mortal once again, but would be able to live out the rest of their natural years and then die in peace.

As to the greater question of if their act of unspeakable evil to become a lich can be forgiven...in the spiritual sense, the Book of Exalted Deeds states that no being is beyond forgiveness if they truly seek to repent - at least, not in the eyes of the forces of planar Good and the gods of that alignment. Forgiveness from the lich's victims is another matter entirely.

A Note for Pathfinder Games

Pathfinder's alignment system is essentially just 3.5s; however, the developer's attitude towards it tends to be more consistent. Sean K. Reynolds, Jason Buhlman and the various Pathfinder writers gleefully embrace fantasy racism and the idea that a being or being(s) can be born irredeemably evil. That doesn't have to affect how you run your game, but tread lightly in Pathfinder Soceity games.