Is the Lich King a Lich?

Before Arthas donned the Lich King's armor, it was the spirit of the former Orc Shaman Ner'zhul whose soul was attached to the armor and then imprisoned (physically) inside the Frozen Throne. Now Arthas and Ner'zhul's spirit are one and together they are the Lich King.

Was the Lich King a bad guy?

The Lich King is a powerful entity of evil in the Warcraft universe who is the leader of the undead army known as the Scourge.

Is the Lich King Arthas or Nerzhul?

So the Lich King is both Ner'zhul and Arthas, but evil Arthas is in control, he retains the powers and memories of both Ner'zhul and Arthas. Then unfortunately, he died, and Bolvar Fordragon was made the Lich King.