BBEG with powerful artifacts - enough to adjust CR?

[MrFahrenheit]

...and if so, how?

So I've begun scratching the surface with how the final boss battle of my campaign will go. The BBEG at the end will be a lich in his lair (a crumbling old throne room in a decrepit castle, abandoned in the wilds, of course!)

The good news: said lair-based lich has no phylactery to retreat to, even if he is otherwise fine (this is due to an earlier quest the PCs undertook).

The bad news: he also possesses the hand and eye of Vecna, attached as they should be.

So does the no-escape clause of the encounter for the lich balance the super-powerful-artifacts clause? I'm thinking not. Is one more CR up fair (which would bring the lich to CR 23), or is it really of no consequence at this high level?

(Other note: the party will have had two combat encounters, effectively in a row, before this fight. They'll get a short rest after battle one, but not between battle two and the lich fight. This is important; otherwise, at level 20, the final boss would probably be a cake walk regardless of artifacts and lairs).

[ShikomeKidoMi]

Well, let's see: Not having a phylactery in no way effects the Lich's combat abilities and the players would get full XP for beating him if he had one and was revived by it. If anything, not having one forces the Lich to forgo suicide attacks since he can't be sure to come back afterwards. So that doesn't effect the Lich's CR.

As for the Hand and Eye of Vecna, what we need to do is compare their effects to what the Lich is already capable of.

First, the spells: They don't increase the lich's abilities much. In fact, many of the stronger ones already appear on the Lich's spell-list. And he's not so low on spells that they additional casts of things like Disintegrate or Dominate Monster are a huge boost.

So what about the other effects? Is having Truesight, regeneration 1d10, 20 Str, an additional 2d8 damage on melee spell and weapon attacks, the ability to instantly reduce any opponent with a skeleton to 0 hp with a single touch attack if they fail a save, and immunity to surprise worth +1 CR? I'd say so. I'd rate it more than +1 for the instant death effect if Lich's couldn't already take someone completely out of a fight with their Paralyzing Touch. As is, it's mostly the extra 2d8 damage, 1d10 regeneration, +2 to hit in melee from the strength boost, and immunity to surprise that make me think his CR should go up a little but not more than 1 since he's already so high level. It seems a similar increase in power to fighting him in his Lair and that's +1. The truth is that I'm just eyeballing it, though.

If you rolled for particularly useful minor beneficial properties or particularly harmful minor drawbacks, it might adjust things slightly up or down.