- Tirion's Gambit
And now I learn that it might be Arthas's own heart... a thing containing the last bit of his remaining humanity.
Meet me at the cathedral's entrance. Be sure to bring a cultist's hood -- we're going incognito.
Light be with you, <name>.
I do not view what we just went through as a failure, <name>... quite the opposite.
This quest commonly bugs out, with Tirion and his adds frozen inside. This was a known issue as of January 2009. 
Cultist Acolytes are patrolling up and down the stairs of the Cathedral of Darkness, just to the northwest of Icecrown Citadel.[46, 76]
Tirion is up the stairs to the right, by the bonfire with the other disguised crusaders.
The Lich King ends up coming and seeing through the player's and Tirion's disguises. Tirion approaches him and deems his heart to be unredeemable and thusly strikes it down. Destroying the Lich King's heart causes the Lich King to drop to 30% of his health, and also causes Tirion to be knocked out. Darion, Koltira, Thassarian, and some other random death knights end up coming to save Tirion and the player from a rather large number of elite mobs. They will open an "Escape Portal" - Take it, or else the Lich King will instantly kill the player after he casts a 8 second spell called "Lich King's Fury".
To complete the quest, return to Tirion at the Crusaders' Pinnacle. He also explains his reasoning for destroying Arthas' heart. As the title suggests, he assumes that The Lich King didn't destroy Arthas' heart because it could affect him in a bad way and even without anything else to support his assumption, Tirion takes the risk and destroys the frozen organ.
Warning: DO NOT drop the Cultist Disguise buff while inside the Cathedral. An undisguised player will aggro the room and wind up dead fairly quickly. Let the death knights and crusaders do the killing. It's much more enjoyable to see Darion Mograine absolutely dismantle the cultists anyways.
- There you are. Are you ready then? Once we start, there is no turning back.
- Highlord Tirion Fordring says: It is time. May the Light give us strength.
- The party pauses outside the cathedral proper for just a moment before continuing.
- Highlord Tirion Fordring says: Keep your heads down and follow my lead.
- Highlord Tirion Fordring says: Here it comes. Stand ready.
- Fordring leads the party to one of the pews as they wait for the Chosen Zealots to walk in and approach High Invoker Basaleph, laying the heart before him. As the zealots leave...
- Chosen Zealot says: We lost many to the faceless ones, my lord. But we succeeded in retrieving the heart from Naz'anak.
- Highlord Tirion Fordring says: Something's wrong... I sense a dark presence.
- Tirion turns to look at the doorway as the Lich King enters.
- Highlord Tirion Fordring says: The Lich King is here. May the Light guide our blades.
- The Lich King approachs Basaleph, then turns to look directly at your party.
- The Lich King says: Uninvited guests! Did you think you'd go unnoticed inside my dominion?
- There's no point in continuing the ruse, so Tirion takes the Ashbringer in hand and walks right up to Arthas.
- The Lich King says: I must confess... you were not altogether unexpected. I hope you find your final resting place... to your liking.
- Highlord Tirion Fordring says: You sound a little too confident. Especially considering the way our last encounter ended.
- The Lich King says: Last time we met, you had the advantage of fighting on holy ground. You'll find that our situation has been... reversed.
- Highlord Tirion Fordring says: That might be, but I don't need to stand on holy ground to run that disembodied heart of yours through with the Ashbringer.
- The Lich King says: I call your bluff. You're a paladin after all. Your obsession with redemption goes beyond the inane.
- The Lich King says: You surely wouldn't destroy humanity's only chance to redeem its most wayward son. You'd sooner die!
- Highlord Tirion Fordring says: The heart... the last remaining vestige of your humanity. I had to stop it from being destroyed. I had to see for myself. And at last I'm sure...
- Highlord Tirion Fordring says: Only shadows from the past remain. There's nothing left to redeem!
- Fordring charges the heart and runs it through with Ashbringer, knocking himself out, killing Basaleph and blasting the Lich King away as the heart explodes, dropping the Lich King down to 30% health.
- The Lich King yells: Arrrrggggggggggh!!!!
- Disguised Crusader yells: Tirion's down! Defend him with your lives!
- The three Disguised Crusaders rush forward and take defensive positions around Tirion.
- The Lich King yells: You... will pay for that, old man. Slay them all!
- The room full of NPCs circles around the party. Suddenly <Thassarian/Koltira Deathweaver>, Highlord Darion Mograine, and a group of death knights run into the middle of cathedral.
- (Alliance): Thassarian yells: I hope you fellows don't mind if we crash this party. I brought some old friends with me!
- (Horde): Koltira Deathweaver yells: Take courage, crusaders. You do not fight alone!
- The friendly death knights dispatch the room. Darion then runs up and opens a Death Gate to Crusaders' Pinnacle, turning to look at the Lich King.
- Highlord Darion Mograine says: Quick, through the portal! He won't stay down for long.
- (Alliance): Thassarian says: Looks like whatever Tirion did put some hurt on the Lich King. It's too bad we can't finish him off....
- (Horde): Koltira Deathweaver says: The Lich King is badly hurt. We ought to stay behind and finish him.
- Highlord Darion Mograine says: Patience... we will get our chance soon enough. Be content that for once, it is Tirion who is in our debt.
- The party takes the portal before the Lich King finishes winding up the Lich King's Fury, which would instantly kill anyone foolish enough to remain behind.
According to the combat log, Lich King's Fury "instantly kills" anyone it hits, rather than actually doing damage. If you use Spell Reflection on it, you will still get the message in your combat log, but will not actually die. However, the Lich King will immediately teleport away.