A Liche is a type of undead creature. Although similar in some respects to a Zombie, they are in fact quite different from them, as unlike Zombies, they retain their intelligence, thus making them far more dangerous. At times, they can also practice powerful acts of magick.
The Roman Legionnaire Pious Augustus became a liche after making contact with one of the Ancient Essences (which one depending on the player's actions). As a result, even though his body decayed to resembling a skeleton in Centurion armor, it embued him with either the ability to revigorate his dead body and level buildings, render the ground asunder, as well as wield power mortals could only dream about with a mere touch; the ability to read minds and drive people mad as a result; or significant understanding of the multiverse to such an extent that there was neither a mountain too high for him nor any city too far from his reach, as well as giving him powerful enough Magick to bind Mantorok in place with his own magic.
Ellia, as a result of both Pious' murder of her and her taking into custody the Heart of Mantorok, became a Liche. Ellia, however, had slightly lesser abilities compared to Pious, being able to move only in a very limited manner (when supplying Edwin Lindsey with the Heart of Mantorok, and presumably to get to her hiding spot), although she had enough magical power to project Mantorok's power via a nearby statue to knock Pious away and force him to retreat.
The Bishop was implied to have become a Liche by the time Anthony fought him underneath Oublié Cathedral as a result of his authoring the curse intended to go towards Charlemagne the Frank and intercepted by Anthony, since he was undead (evidenced by his glowing eyes and sapping sanity), as well as retaining enough lucidity to ask Anthony if he came to return his book and to offer to put him down, as well as summoning two super-zombies to attack him.