Mag does have his shield, and he can use a bunch of other outside material for the fight, but he has never gone against an opponent of the Lich King's magical caliber. This one will be a good fight. Mags likely has the advantage since he can try staying out of range, but I'm not convinced he could really do much damage to the Lich King.
http://www.wowwiki.com/Lich_King
Not 100% accurate, but the outline is there.
As to his exact abilities they weren't clearcut like comic books, we know he can make portals into other worlds, his body was torn away and replaced with a ridiculously strong armor of ice, and his mind was granted awesome powers. Being a lich, he obviously had powers of wielding the undead and bringing about "The Plague." He could mentally dominate those that he touched.
Arthas used Frostmourn to slay a whole crapload of enemies, the sword eventually drained his soul and made him an undead. He defeated Illidan and took on the old Lich King's helmet, effectively fusing Arthas and Ner'zhul, becoming the most powerful entity on Azeroth.
I think the Lich King would win with not too much effort. One of the mightiest beings ever in the Warcraft era was Sargeras, with only his eye Illidan could blow up the roof of the world. Now in the WOW manual it says that the Lich King combined with Arthas is the mightiest (at least one of) being ever, I can't see Magneto beat that, especially not when he can't use his greatest powers against him.
Magneto could attempt to bury the lich under the Earth. Thus negating his threat level. Then again the lich could just make a portal and get out.
Magneto could attempt to make the few cells in the lich'es body vibrate to the point of explosion. But sense he's undead, those cell's might not in enough amount to "kill" him as his body won't be fully anniahalated. And there is no second chances in this battle.
Magneto has not the time, nor the exact oppurtunities to win this battle. Which is a damn shame, SpellJammer is an avid fan.. but lich king wins.. hands down..