Oh my!
You used my used my bardic lich idea! Gonna make me blush.
Going along with that theme I thought it'd be neat to have alternative "liches" for different types of magic.
Illusion liches that exchange their bodies for semi-real illusions. Their phylactery could be a permanent illusion somewhere in the world, from a bird on a tree to a whole small village that doesn't realise they're illusions.
Cleric liches that become eternal beacons for their god's faith and power, their body withering away to become like those mummified monks but ablaze with channelled divinity. Protecting the holiest of temples, giving council and wisdom or actually leading a church, even being worshipped as a demi-god.
Less magic school-specific but I also thought some kind of book/text/story could contain a powerful spellcaster, sort of another kind of memetic lich like the bard one.
For a paladin lich, what about becoming their holy sword/shield/armour? Guiding/possessing new generations of heroes for great threats.
There's actually a brain in a jar undead along that lines.
Alternatively, there's a prestige class to turn completely incorporeal and a race that already has the ability. A disembodied mind works as well as a brain in a jar imo.
I had similar thoughts for summoners. Them "unsummoning" themselves from the world, hiding their soul out in the planes and only acting through a summoned fraction of their being.
>You swap bodies with other younger people, controlling their minds permanently
There's a psionic power like that.
I had similar thoughts but along the lines of a barbarian who dies while raging and just never notices and stops, there's actually an ability for the frenzied berserker prestige class that lets you fight past death for the duration of your frenzy.
In some versions, normal liches actually already rebuild their body from corpses left with their phylactery.