The lich (rhymes with “itch,” not “ick” or German ich) stands out not only as the alpha undead creature going all the way back to the days of Advanced Dungeons & Dragons but also as the only type of undead creature that’s undead because it wanted to be. It’s what you get when a wizard decides he or she wants to be immortal, reads the fine print on the contract, and says, “Yeah, I’m down with that.” To become a lich to begin with, a wizard must necessarily be monomaniacal, as well as malicious, sadistic and/or vengeful, and the transformation of undeath intensifies these traits. A wizard who becomes a lich must also necessarily be a genius and a world-class spellcaster, and the lich retains these traits as well.
Although it’s only as strong as an average humanoid, all of a lich’s other ability scores are exceptional, most of all its Intelligence. It gets sizable bonuses to Constitution, Intelligence and Wisdom saving throws (notice that two of the “big three” are in that bunch); resists cold, lightning and necrotic damage; and is immune to poison damage and to physical damage from nonmagical weapons. It can’t be charmed, frightened, paralyzed or poisoned, and it never suffers from exhaustion. It has truesight—the ability to see in darkness, into the ether, and through illusions, transmutations and invisibility—out to a range of 120 feet, along with a passive Perception of 19. And it’s proficient in both Perception and Insight, so not only does it notice you’re there, it knows what you want.
A lich receives additional, powerful lair actions when it’s encountered in its lair. Why, then, would it ever leave? Good question. It won’t, if it can help it. No lich will ever leave its lair unless it must, in order to do something that it can’t get an agent to do for it. Follow-up question: Who on earth would sign up to be an agent of a lich? Well, who on earth would sign up to be an agent of Adolf Hitler? The answer is, someone of like mind—in the case of a lich, another evil wizard hoping to gain access to its voluminous reservoir of arcane knowledge. Or someone who considers the lich’s long-term goals to be aligned with his or her own. Or someone who fears the lich’s power and hopes that he or she can earn privileged treatment by showing sufficient loyalty and obedience. (Spoiler: Not likely.) Or, barring all that, someone whom the lich has magically dominated. Agents of a lich must be powerful enough for it to consider them useful, and they’ll generally be ambitious enough for service to a lich to seem like a reasonable arrangement.