If you havn't got the cash and want the free pack this is the easiest way.
This is how the game plays out: the King plays some 3/4s and 2/2s to try and dispute the board after he wastes his 1st turn, meanwhile you should be drawing into cards that give you empty mana crystals, and on turn 4 you should have Jade Behemoth out, then throw behind him a Gadgetzan Auctioneer and cycle through the rest of your deck. Nourish is there to speed that process up even more. If through some freak accident he clears the board, just try again and hopefully he won't draw into his removal spells, which he often times keeps for your bigger threats anyways.
Remember that the Lich King will start by clearing his board on turn 7, so if you can have a taunt your [card]Gadgetzan Auctioneer [/card] is safe. You can maximize the auctioneer's turn by having 8 mana on the turn he acts this way. Should be plenty to fill up your deck and put down some big threats.
Also keep in mind the Lich King doesn't have any spells that can deal damage to the face; if you can make it to the next turn, even with 1 HP, go for face, and chances are he will attempt to clear your big threats.
- If you've got Fandral Staghelm he helps a lot, but he's not necessary.
- Tree of Life might help a bit too, just because after turn 7 you might be running low on health.
- If you've got Feral Rage, take it instead of Healing Touch.
- If you're struggling to make it to turn 7, or life long enough past it to cause real damage, give Jade Blossom a hoop and take Mire Keeper in its stead.
Might take a couple tries, but it'll work.