My English is bad so I'll try my best to explain the combo.
So your only minions are, Mecha'thun, Stubborn Gastropod and Alarmobot. You can fill the rest of the deck with any spells since Lich King is going to destroy them on turn one anyway.
Mulligan: Stubborn Gastropod
The Gastropod is here to protect the Alarmobot, you need to play it on turn 2 (Since Lich King basically destroyed your deck, even if you didn't keep Gastropod at mulligan you still got 1/3 chance to draw it on turn 2)
Then you need to play Alarmobot on turn 3 in order to summon Mecha'thun on turn 4.
The Lich King is going to kill your Alarmobot even if you don't have any minion left in hand and then you just have to trade your Mecha'thun into his minion (he might do it himself).
For me, it worked after 3 tries (died from fatigue damage before killing my Mecha'thun), I hope this can help some peoples:)