A Complication and a Question

[Seisho]

The complication is mostly for the players - imagine following scenario

You've got an Lawful evil Spellcaster that has just completed the ritual to create a phylactery and become a lich. Instead of hiding it in some dank cavern the phylactery gets an additional enchantment hiding it's magical aura or letting it look like a different school of magic and then goes to:

a) The vault of the local Abadar temple. The Lich (still looking human at this point) makes a legetimate business with the temple and pays money to them to safekeep the item in their vault. Now and then he might has to renew the contract posing as his own descendent with a simple disguise spell.

b) A nearby Museum with good security measures. The Lich dupes the Museum staff into believing that this is an exotic and valueble artifact (not wrong, technically) Now it is on display for the whole world to see and at the same time under high security

Now the players have to deal not with the lich but with either part of the abadar priesthood or the museum staff

The question that came to me while making this up was the following - I've read at some point that liches if they continue eating and drinking (and sleeping?) properly basically keep their looks and don't start to decay as that comes from neglecting the body and relying on the necromantic energy to keep you alive
I am just not sure anymore if that was pathfinder or another fantasy system

[Ascalaphus]

Liches are all different, that's kind of their thing. They aren't created by a standardized spell or transmission of a standardized Create Spawn effect.

The rules of course give them all more or less the same stats, but the lore is that each of them did a lot of research and found their own personal ritual to make it work. So it could be that one lich can keep their body quite lifelike, while another one is a total skeleton.

So you can choose for this particular lich whatever works well for your story. (I like these complications by the way. Since liches are notorious for paranoia and craftiness, you could even do both, where one is just a decoy or even a trap.)

[Temperans]

There is honestly a lot of potential in how you can run things or even the things you can add (until Paizo does it). When I searched for liches to see their appearance they had many different styles. From just skulls (demiliches), to runescared apparitions (psychic lishes), to mummified look, to those that look more like dhampirs, to normal looking, or even rotten flesh.

But if you look at the rules however, something does stick out:

The process to make a demilich is that the lich's soul does not return to its body, either staying in the phylactery or wandering through places. During this time body decomposes, and if the lich's soul does not return in time the body turns to dust leaving only a skull behind. To me this sounds like the #1 cause for their body to deteriorate is their soul not being in their body.

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Those two plot hooks sound awesome. I can also see something like the lich hiding the alignment and giving the phylactery to some religious order. This would allow the lich to literally hide under the enemies noses.

Or imagine if it were to be taken to some storage only for it to be forgotten/misplaced. (Happens to a lot of art and objects)

[Ascalaphus]

Ooooh I like that idea.. Lich gets smacked down by party, and has its minions ready to support it on its respawning location.. except its phylactery was moved elsewhere and now it respawns elsewhere and the PCs get to take out some confused lieutenants more easily. Followed by a scramble to find the lich before he gets back to a supply stash.

[SuperBidi]

Even if disguised, I can imagine someone will want to study the phylactery and end up discovering that the ancient mwangi artifact is not exactly that.
For the vaults, I think Abaddar church is quite ready for it. Many people use bank's vaults to hide stolen goods or illegal items. I can even imagine a branch of Abaddar's church run by a Lawful Evil Cleric of Abaddar who's specialty is to keep such kind of items. After all, if the Lich pays and as long as it's not messing too much with civilization, I don't see why Abaddar would object.