The Lich's movement pattern is strictly forwards and backwards. It has a number of special abilities:
Fireball: Shoots a fireball straight at the player. Cast occasionally.
Doom: Shoots roughly 7 skulls, one after the other, at the player. Skulls are blockable and will be destroyed by Holy magic. Cast occasionally.
Laser Eyes: Shoots a beam of lasers continually at the player. This beam does not inflict Damage to the Player but remove positive status effects (for example Berserk, Barrier or Haste. Before casting this beam, the Lich will retreat a bit, and wipe back his hood. This helps timing your buffs so they don't get instantly removed.