All levels. A lich should never be a level-appropriate challenge.
I want scary undead to be as scary as possible.
I think this is a very good point to think about.
I don't mean I necessarily agree on a
Lich specifically (but I do agree), but I mean that we should keep in mind that
some monsters may deserve to be considered "inappropriate" in one of the two following possible senses:
a- unbeatable, at least without some external help
b- very tough i.e. with a good chance of failure
For my personal tastes, a deity is always unbeatable, and a lich should always be very tough but not generally unbeatable.
But we have to keep in mind that each of us would put different monsters in the a-league or the b-league above.
Which is why it's not always easy for the designers to choose a monster's CR, and IMHO they made an
excellent choice in 3ed when they made vampires, lycanthropes and liches into templates (although the original reason for doing so was definitely so that they can be applied to any base creature), because these are iconic monsters that gamers have wildly different opinions on how strong they should be! In someone's games vampires should be at the pinnacle of the monsters hierarchy while in someone else's games maybe vampirism is a common as flu and being a vampire just makes you only somewhat more dangerous than before.
Of course this could theoretically be said about any monsters, but some are subject to this much more than others because they have many different incarnations in literature. As far as I know there isn't any literature where kobolds are uber or where beholders are wimps, for instance.
Therefore I can easily say that a Lich should be powerful and scary, but how much... I don't know.

Because 10th level may be good for me, since I usually have troubles DMing at very high levels and I still want Liches to be beatable, but 20th may not be enough for GX.Sigma. I sincerely hope that a variable level is supported as easily as it was in 3ed for these types of monsters...
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BTW this doesn't actually answer [MENTION=14391]Warbringer[/MENTION] question

He specifically assumes an 18th-level Lich and is essentially asking at what minimum level the PC party should be capable of handling such encounter. This question actually has got nothing to do with the fact that the encounter is a Lich rather than something else
I don't have an answer for this. I'm used to 4 being a reasonable max difference between PC party level and encounter CR, but for a more "run!" outcome I think at least 6 is needed. But with 5e bounded accuracy, the number might actually be more.