Obtain a Candle of Beckoning. Summon Lillith Nefara and kill her. Return to Gunther on his island.
You say you are not bound by the will of the Lich King, and the enchantment Bethor placed upon my book corroborates this. But before I believe you I must have proof that you are enemy to the Scourge.
There is an old, bloody altar just off the southern coast of this island. it is used by a powerful Scourge agent, Lillith Nefara.
Take a Candle of Beckoning from this crate here. Light it on the altar and Lillith will awake. Destroy Lillith, and I will believe you are the Lich King's foe.