im working out a story and was thinking of writing in a good Lich, who’s maybe chaotic neutral, but extremely cunning and wise. He is freed by a sorcerers apprentice and I was thinking of them bonding or something. What do u think? 

A Lich will degrade into a Demilich if not fed souls once a year, so you'll need to find a loophole for that. Maybe their soul is that of a unique species who's souls don't degrade, but even if that is the case, they'll probably still feel the urge.

If they have been imprisoned for a long time, they'll be seriously out of touch with the present. You could play this as a Fish out of water comedy, but most liches become undead due to thirst for knowledge and/or power, so as soon as they're free, their first priority will be learning everything

Speaking of, how did he turn? Did he do it willingly? If so, how does his alignment reconcile with the inherent evil nature of the ritual of Lich-yness? Was he forcibly turned by someone else? If so, why? What reason could anyone have to turn someone else into a Lich? Maybe they have his phylactery, and want to force him to do their bidding?

If you don't go for that, where is his phylactery? Is it with him when he's freed, or is it kept somewhere else?

As for personality, I'd personally play him as a bit of a senile old man with a love for joking and making fun of the youngsters. Maybe he's trying to teach them a lesson in a Mr. Miyagi-way? Or maybe he's more "You darn kid-adventurers get of mah property!", but deep down cares about them?

Let me ask, what does it get you for him to be a lich, rather than, I don't know, a Star Wars Force Ghost or a time-displaced wizard or something?  If this is a story you're writing, any relationship between a young person and an ancient rotted talking corpse is going to be a little hard for the audience to ride with.  

You raise a lot of good questions, I’ll try and answer the in due time, let me just think for a little bit.

but, he wasn’t turned willingly.

Conventionally, being turned into a lich is a process which not cheap or easy. It is also giving someone tremendous power and immortality. Your game, your decisions, but conventionally, becoming a lich is something you have to pursue as... a once in a generation ambition.

That said, if the character has to be a soul-sucking undead superwizard, then why do they have to not be evil? Evil doesn't mean stupid. Evil doesn't mean short-sightedly destructive. An evil character can be benevolent, they can be reasoned with, they can be on the side of the heroes. An evil character can be anything if they have a strong reason to do so. An evil character should only kick puppies when they are powerful enough to avoid repercussions. Evil should be insidious and, if they are immortal, then their plans can take generations to see fruition. Why not? They have time. No reason your lich couldn't play ball with the heroes, even as a soul-sucking undead.

I'm with SigrunOfTheBorderRealms, TimCurtin, and Verenti on this.

It doesn't preclude a Lich coming to a reasonable conclusion to shift alignment somewhere in its long unlife. If it were me (and it's not), I would need a long road back and something significant to take that first step. A Lich's existence has certain needs that will conflict directly with a Good alignment if some reasonable workaround is not designed into the character's history (again, if it were me and it's not). Even still, a Lich is a Lich to most inhabitants of the Material Plane. I would need to factor some influence based upon that in some way.

It's not impossible, but TimCurtin's and Verenti's questions are very important. How important is it for the character to actually be a Good alignment rather than an just an aligned goal? It is my belief that the answer to that will provide reasonable options.

Here’s what I'd wanted to happen: he was never evil, his master tried to commit a ritual to make himself a Lich and tried to use his apprentice's soul among others to do so. But something went wrong when the apprentice interrupted the spell and reversed on his master, making himself turn into a Lich. This results in him being entombed against his will in a ruin, until someone frees him. But he was never evil aligned. 

A common theme among Lich lore is that the Lich must personally and deliberately do something Evil in the process of becoming a Lich — something abominable like the bloodletting and eventual slaughter of a live infant or something.

Maybe a Lich isn't what you're wanting but, rather, some event gone awry creating an undead mage of some equivalency. EDIT: Possibly one that is mistaken for a Lich or even one that considers itself a Lich erroneously.

Here's a thought: Arch-Lich. While the process to becoming one is nearly identical, only Good-aligned people could do it and the Good adjustment in the process would leave them weaker than their Evil counterparts.

There's still the whole deliberate component of it so that an accidental Arch-Lich is unlikely unless the character is unaware of what is going to happen.

A deceived but Good-aligned person involved in the Lich creation process might discover the true nature of the ritual (like discovering that the person being assisted is Evil and is seeking immortality but the Good character does not necessarily fully grasp the whole Lichdom process) and do something to stop it. Since that person would have been personally involved in the process but not directly involved in any of the Evil acts required, such a person might accidentally get turned into an Arch-Lich during the attempt to foil the ritual.

So, it's possible, but it's not exactly the same as a Lich who must do something vile to gain vast powers unchained by moralities.

Perhaps a godly power (or something potent and divine) intervened during the lich process which stopped the original caster from turning but the magic had to go somewhere.  Your poor unwilling lich happened to be the new target of the spell, which may or may not have been the intent of the entity that interfered with the spell.  Ripping the poor apprentices soul from its home and trapping it in some kind of phylactery.  They have have even felt bad enough about what they did that they sealed him up till a day when someone could do something for him (what that is i dunno) maybe just be a chance for him to do something great in this world.  Nothing saying that how they sealed him up couldn't stop or slow the demilichification process.  Either that or they have been feeding it some kind of soul stuff to stave off that process.  Or heck make him into a talking skull like BoB the Skull from Dresden Files.

i misspoke when i called him a Lich, i meant an archlich or something similar.

Don't get too caught up in the semantics, you want someone non evil who is cursed/blessed with unlife  of the possibly eternal variety.

Don't allow yourself to be too constrict with the rules around cliches, there are exceptions to every rule and it's your game. 

Were there still some specifics you wanted to hammer out for your undead buddy?

https://www.reddit.com/r/dndnext/comments/dou3oy/lich_writing_help/