I don't believe he is a lich in any sense of the word. We have two lich-like characters already who follow the different paths of what a lich is, but Morde doesn't follow either.
Based on how the black mist of the Harrowing treats corpses it seems likely the souls of the dead reside within the corpse in Runeterra, meaning if Mordekaiser's armored wraith form is destroyed his soul would return to his remains. If his skull was destroyed the list of remains he has left would be smaller, and so his skull would no longer be needed. With that said if part of the total remains was still in existence, but not present, the ritual would be impossible to complete.
Destroying all but one piece of the skeleton would make it far easier to keep track of his remains, however it would also make it far easier to fully destroy him. While not specifically mentioned my guess is that the mages who raise Mordekaiser when he dies each take care of a portion of his remains, so that even if one is found there are still pieces left for the ritual elsewhere.
He doesn't have to worry about this on the Shadow Isles, of course, but it seems like something someone willing to build an enormous, fortified tomb would do. If true it's possible the thief also only found a fraction of his remains.