Okay, right now, you cannot fight the Lich King. You meet him several times during the completion of a number of quests, but you can't actually (to the best of my knowledge) enter the Icecrown Citadel and fight him yet.
( Vile speculation and possible spoilers if you haven't done the Angrathar the Wrath Gate quests yet )
( Vile speculation and possible spoilers if you haven't done the Angrathar the Wrath Gate quests yet )