OK, sense, barely anyone knows... about how much fucking lore i know about Warcraft, i will make this sad but true story short.
Deathwing is the earthen brood father of all of the dragon aspects, and leader of the black dragonflight. deathwing in WC2 was captured and controlled by the old horde, and was used as a wrecking ball against the alliance in the southern half of the eastern kingdoms. in WC3 he disappeared and hasn't been seen until "The Shattering"(WoW patch).
and we all know about "The Lich King"
The Lich King is now dead, thanks to ICC10(25) so basically Deathwing wins by default. he he
Uhm, no.
First of all, Deathwing fought for the Horde in order to make a devastating blow against the other three elements since he is an element as well.
There's the element of time, of life, of Magic (?) and of Chaos.
Deathwing is the element of Chaos, and therefore his only purpose is to cause chaos.
Basically, Deathwing started a huge-ass war with the Burning Legion ages before Humans and Orks moved into the world, and in order to win this war, he had to convince the other elements to fight along his site with their dragons.
After the dragons won that war, Deathwing created a holy artifact possessing the essence of all four elements, and with that he slaughtered every dragon apart from his own. This way, he also banned all other elements into their places and has full control over them.
The one you think that was captured by the Orks is the element of Life, whose name I forgot. She bred loads of dragons for the horde in order for them to cause chaos around the border of azeroth and to scout out the area around their bases. In the first WarCraft book, that dragon is set free by some random human, and bans Deathwing into a different dimension (again). That's when he disappeared, just in order to appear again during WoW.
Just as a bonus nerd knowledge, the element of Magic, Saphiroth (or something) is killed by Arthas during the events of WarCraft III, meaning that technically, nothing can stop Deathwing.
In WC3, he didn't appear at all, since his existence and downfall happened years before Arthas' rise to the Frozen Throne, since he was a little child during these events.
The Lich King is not "dead".
Arthas travelled to Northend in WC3 in order to save the Lich King from Illidan's forces that seeked out to destroy the "geissel", which were the minions of the Lich King.
At the end, Arthas causes Illidan to be seriously injured and leaves him behind to die, but Lady Vash and Kael'Whatevertherestofhisnamewas save him and restore his powers, which causes him to get completely insane over the mass slaughter he has done. Whatever.
Arthas walks up the giant-ass Frozen Throne, where the Lich King resides. Arthas theoritcally kills the Lich King in order to get his helmet and powers, causing him to be the leader of the geissel, as well as the new Lich King.
tl;dr
Lich King isn't dead.
