like what would happen in this situation? 

You have a lich with a high charisma score.  That's what happens.

Xykon. But, seriously, the biggest reason they've tied Lich to Wizard in 5e is because part of the concept for the lich is (and should remain, but that's a UA topic and probably doomed in any case) that as enemies who have the potential to be ongoing villains, they can trade out their prepared spells to suit the current scenario. Wizards can do that, Sorcerers can't. Plus the idea of undergoing rigorous study and preparation to become a lich falls more into the Wizard field than Sorcerer. And, finally, it would be tricky to reflect Metamagic on an NPC block as a concise feature.

NPCs don't have to follow PC rules, though.

The thread’s title is a bit ambiguous: is it asking whether sorcerers can become Liches or whether the origin of a sorcerer's powers might be, in some way, a Lich? 

If you have some time have a look at a small series of videos Pointy Hat did on youtube about doing Liches for various non-wizard classes, I think he did Sorcerer, Barbarian, Ranger, Druid and Artificer as well as a general "problem with Liches" video but I found the one that turns a Barbarian into a Lich particularly interesting.

Quote from ThelenyiWhinlaw >>

The thread’s title is a bit ambiguous: is it asking whether sorcerers can become Liches or whether the origin of a sorcerer's powers might be, in some way, a Lich? 

 its meant to be what happens to a sorcerer if they are the decendent of a lich. 

i heard someone say that they might not have working...(you can fill in the rest).  so not sure about how that works. same person said it would be a "test tube child" situation.

Quote from imakestuff >>

Quote from ThelenyiWhinlaw >>

The thread’s title is a bit ambiguous: is it asking whether sorcerers can become Liches or whether the origin of a sorcerer's powers might be, in some way, a Lich? 

 its meant to be what happens to a sorcerer if they are the decendent of a lich. 

 
Liches are undead. They can't have descendants after becoming undead.

If you want a sorcerer with an "undeath" theme, that's already been done officially: the Shadow Magic sorcerer. They are linked to the Shadowfell, the plane of undeath and darkness. 

I still think it would be fun if one of the party members secretly had a past like that. like he starts as a bit of an edgelord bet then you learn WHY he is a bit of an edgelord.

I don’t think there is an absolute rule that Undead can’t have descendants. There are a few examples (not necessarily D&D ones) of Dhampirs being conceived by the “conventional” process, so you could use that as a precedent for fertile liches. 

Alternatively, a lich might bless/curse a favoured/hated bloodline with sorcerous powers. 

Or, for Terry Pratchett fans, you could argue that heredity doesn’t always work the expected way (e.g. Susan Sto Helit). Perhaps a lich adopted a child, and their child mysteriously exhibits some of the lich’s powers. 

or, they are just a homunculis. the lich used their dna and some other parts to create an artificial creature. 

I think there's a mistake conflating sorcerous origin with bloodline. While some sorcerous origins are flavored as some sort of birth lineage, an examination of the origins shows that's not a universal case.  So, sure, a lich could do something that leads to an effect with a being becoming imbued with sorcerous power, but that's a separate question from whether and how a lich as a lich could have offspring.  And really the answer to that question comes down to the workings of individual game's worlds.  Clones, reborn, damphyr all seem easily in reach options, any of them could be seen as a "lich child".  Maybe it's a straight up Palpatine situation, where the "lich child" was supposed to be a vessel for the lich but somehow escaped that fate, for now at least.  There's a plot hook. 

still, what would happen and how?

Quote from imakestuff >>

still, what would happen and how?

 The universe ends and a new, even weirder one takes its place.

Seriously though, there's no rules about it so it would be up to the GM.

Still unclear about whether we’re talking about if there should be a lich subclass for sorcerers or if we’re now talking about if someone is a descendant of a lich. Or maybe both?

The descendant thing, they could have had children before they became a lich. I guess that’s not going to mean some kind of lich genes passing on, but it’s possible that way for a lich to have kids or grandkids or however many generations you want. 

For a subclass. Sure, maybe you were a lich’s servant and just being around that kind of magic some of it seeped in. Or the lich lived in the sewers under your house, and its energy flowed through you — like lead paint or other toxic waste. Or you were the subject of experiments the lich was doing. Lots of ways something like that could happen.

You could go a pseudo-Voldermorte horcrux route. The Lich, alongside creating a phylactary, splits his soul into several parts and places those within other mortals via some, thought to be, forgootten ritual. as long as one of those mortals or their decscensants live, the Lich will "live" forever. If the lich is killed and his phylactary destroyed, he takes over and subsumes one of the mortal descendants and creates a new phylactary and the process repeats. This gives a DM a recurring villain if they need one and provides some plot hooks for players to investigate as they try and find the sorcerers that house the fragments fo the Liches soul.

The mortals might be a family that suddenly came into wealth some time ago and one child in every generation becomes a sorcerer as they innately channel some of the Lichs knowledge, and the type of sorcerer could be any of the existing ones to represent the vast magical lore the lich possesses but you could also build a custom spell list or homebrew a sorcerer origin for it but for ease I think I would, as nobody seems to like it, port the Undying Warlock subclass over to Sorcerer rather than try to homebrew something from scratch.

EDIT: not to forget there are some goodly aligned liches so this doesnt have to be an evil thing.

my idea is that the lich made an artificial creature using some of his dna. so a test tube child situation. they would use necrotic magic.   

So, a shadow sorcerer then.

Quote from The_Ace_of_Rogues >>

it would be tricky to reflect Metamagic on an NPC block as a concise feature.

Actually it doesn't need to be difficult; I've adapted a few sorcerer builds into monster stat-blocks for running enemies/NPCs, and all I usually do is bake metamagic into one or more spells. For example, a spell that normally only targets one creature can be tweaked to target two (Twinned Spell), you could boost the monster's ranges a bit (Distant Spell), and so-on.

Most monsters don't usually last beyond a single fight, so you don't want to worry too much about tracking resources, plus you normally calculate Challenge Rating on the basis of only three rounds of combat anyway, so it's unlikely they'd run out of sorcery points in that time, so why worry about it?

Not that I think lich makes sense as a sorcerer sub-class; Wizard feels the better fit, especially since every Wizard is pretty much a wannabe lich. 😂