Hearthpwn

Looks like it's a glitch around how the Harvest of souls HP works. The HP makes him immune regardless; there's a trigger tied to frostmourne that says that if all trapped souls are dead, destroy this and get the third HP; as frostmourne was stolen, you get the phase 3 HP and LK does nothing, stuck in P2. Sounds like he's destroyable with stuff like mecha'thun, though.

ETA - this is judging from a wiki. Just don't use stickyfingers unless you're going to mecha'thun, I guess.