Well youre correct on their origin. But knowledge of necromancy isnt completely locked to the legion and the lich king. it isnt just taught by anyone, but there are still ways to learn of it and practice it without being a servant of the lich king or burning legion. Or even someone who was a defector from the Cult of the Damned, as you say in your rp application "Faction: (remember defectors and neutrals exist)"
Now if we spoke of lichs or absolutely all powerful necromancers than youre entirely right that they have to be lich king or legion servants.