Seems like a[ny] "Lich King," who has had decades, if not centuries, to pursue their magical research and expansion would have any or all, as many as you want, custom items.
Some staff that does a bunch of things. Rings/amulets/medallions/bejeweled armbands/et al assorted jewelry that do stuff. Headbands/crowns/headdresses that do stuff. Robes and cloaks. Basically...everything on their person should have some magical purpose.
In this case of this guy who is in charge of a realm of evil mages...seems something to prevent all divinations and mental intrusions would be of significant importance to have on their person/worn at all times.
And that doesn't begin to address the number of personal spells and supernatural effects that have been "permananced" on their person. I believe the Continegency spell specifies that you can only have one active at a time...but that one should be a doozy.
I don't see why an undead wizard dictator who is obsessed with his own immortality would have magic items suited for combat personally. He has an entire army, along with assassins, wizards, clerics, and undead. Getting to him would be near impossible unless you script it. I would give him items that let him evade, escape, and survive. A helm or Teleportation, a cubic gate, a portable hole full of high level undead, etc.
The best magic item is actually found in the Monsters Manual, and this guy needs at least one. The Iron Golem. Increased action economy, good defenses, and its best offensive ability is ignored by the lich.
Other than that, cloak of displacement, ring of wishes, ring of spell turning, rod of absorption, staff of power, a couple wands, is the helm of brilliance still a thing?
Well, he absolutely has to have about 10 minor magic items that don't actually stack with anything but he has fond memories tied to them. "Oh, the coral pendant? This old thing? Oh, it was from the shaman of the lizardfolk tribe I erased about 300 yrs ago. I finally figured out how to use fireball efficiently. sigh... Thanks for noticing! Oh, and, fireball!"
+1 for a cubic gate, a way to escape without teleport. That's kind of done, and gives a hook to a new adventure. Oh, hey, his phylactery is hidden on one of the planes! Best find it before he reforms. He absolutely has to have a killer staff or wand. Minions to respect the action economy, probably summoned or constructed. Artifact level crown that has a jewel that is magical in its own right that can be pried off and used. (The using the crown itself would be ... unwise.) I like the ring of spell turning, especially with the number of spell casters in 5e. Would that affect the spells used for a paladin's smite? That's only one target.