Originally Posted by
Triceron
It's neither canonical nor reflected in the visuals. You don't transform at all, all that happens is your status gets flipped as being Undead and you gain some limited CC breaks and lifesteal perks. It's not a form, and nothing about it involves turning into another creature.
By all means, a Death Knight using Lichborne is still a Death Knight. No different than the Mage's Covenant ability that turns them into a Skeletal Mage. That's not turning into a Lich either, even when they have a visual form. You're still playing a Mage, through and through. You don't ever turn into another class entirely.