Question about Karthus(Lorewise)

So Karthus is a lich, right? I myself did really not know who or what a lich is, and there's no translation into my language(atleast I think so) so I read a wikipedia article, and found this phrase: "Often such a creature is the result of a transformation, as a powerful magician or king striving for eternal life uses spells or rituals to bind his intellect and soul to his phylactery and thereby achieve a form of immortality." Does that mean that Karthus is lorewise unkillable?