|A lich who, having existed for countless centuries, has grown almost unimaginably powerful through the study of dark magic.|
Ancient liches are extremely powerful undead casters with a wide array of resistances and access to several deadly attack spells that can deal ridiculous amounts of damage or summon devastatingly powerful allies. If you are not confident in your skills, escape is strongly advised. Ancient liches can rarely be found on the last floor of the Vaults, in the Abyss, the Crypt, the Tomb, and the Realm of Zot, and are a common sight in the orb chamber of Zot:5.
Tips & Tricks
First and foremost, understand that ancient liches are some of the most powerful casters in the game. When dealing with them, don't worry too much about conserving resources; if burning a consumable or two will greatly ease the battle, do so. A character with Haste and Might, for example, will have a much easier time than a character relying on their skills alone. Berserking is chancey, as ancient liches often generate in places where you don't want to be attracting a lot of attention, but the boost to HP and damage can make a huge difference.
As liches resist most elemental damage, combat casters should rely on pure Conjurations and Earth Magic (although Lee's Rapid Deconstruction, sadly, cannot target them, and their AC is high enough to minimize its shrapnel damage). Necromancy specialists can deal brutal amounts of damage with Dispel Undead, though it requires being at point-blank range and will still take several castings to get the job done. Nearly all Hexes are useless against their infinite magic resistance, so don't bother trying to enchant them.
Melee fighters should wield holy wrath- or antimagic-branded weapons if they are available, and should lure them around corners or use scrolls of blinking to get into melee range as quickly as possible; wasting turns rushing into the fray will result in you getting pounded by brutal attack spells or having various dangerous summons join the fight. Once you get close to the lich, casting Silence or reading a scroll of silence will disable the vast majority of their abilities. Their melee attacks might not be insignificant, but they're a good deal safer than most of their attack spells.
Throwing nets are very useful against ancient liches. Hitting one at the edge of your line of sight with one guarantees it won't be able to follow you for several turns, allowing a fairly safe escape. Hitting one in melee range will make it vulnerable to stabbing attempts, allowing Short Blades specialists to make very short work of them.
Of course, since it's unlikely that you'll be able to take them out without taking a single hit, being able to survive their spells is advisable. Don't go after them while wounded, apply any useful buffs you may have available (Repel Missiles, Haste, etc.) and if your character has any significant holes in their resistances, consider chugging a potion of resistance; it may be wasteful, but taking 100+ damage in a single turn stings.
As always, remember that killing a summoner destroys all its summons. If you are confident you can finish off an ancient lich before its summoned fiends can finish off you, go for it. If you aren't confident of that, consider what safe escape routes you have available.