Liches are undead. This can actually be pretty cool.
Most notably, being Not Alive makes liches immune to quite a few things.Spells like Wither, Dominate, etc. Undead also have 50% unholy resistance, which makes fighting against AV less of a worry. It's much more useful in FF though, as being undead makes you immune to poison (the archos are toast) and all the wold demons make unholy resistance much more useful.
In addition, Undead units can learn Cannibalize, one of the most awesome things in existence. anywhere. ever. In FF, undead can also learn Implacable. Which is basically march, but twice as good (it's incredible), and gives some first strikes too. Undead units can't learn march, but if you're amurites, you can upgrade a lich from a high priest who learned March in life, and he'll keep that after lichdom.
There are, unfortunately, some downsides, though. Being undead makes you vulnerable to that Undead Slaying promotion. Although who ever uses that? It also makes you immune to quite a few positive spells, as well as the negative ones. Courage/Valor/Haste/Regeneration/Bless. The loss of haste really hurts, as a lich will just slow down your army. Although FF has that problem covered by the Force I spell Accelerate, which is basically haste for undead/demons/siege weapons. really useful for khazad too.
Lastly, being undead gives you a significant weakness to holy damage. So using liches in direct combat against mercurians isn't a good idea. And anyone running Order can bless their troops for a nasty sting against you. Also, Crown of Brilliance, already horribly powerful, is a Holy damage spell. It tears undead to pieces.On the subject of spells actually, there's also Destroy undead, whichyou become vulnerable to. Much more acessible, it can be used to attack you even while hidden deep within a stack.
All in all though, I would say that being a lich has some interesting uses, and is in many ways preferable to a living archmage. Many, but not ALL ways. Each is best for different situations.
Oddly, given the resistance to unholy damage, and the fact that most spells which damage you are in good spheres/religions, it seems that liches are actually better off being made by good nations, rather than evil ones. If you're on the side of good, your lih is going to be strong against the things you'll be facing, rather than facing against things designed specifically to kill you.
Bannor Liches for the win!