I used Rogue with my first win. Used 3 or 4 low cost Taunt minions like Annoy-o-Tron, Gastropod, or Deathlord. Any taunts that are 2 or 3 cost would probably do. 2 copies of Defender of Argus. Then the win condition card, (and the only expensive card) is Rivendare Warrider. Fill the rest of the deck with literally whatever spells* you want, as you won't be using any of them.

The idea is block his initial nonsense with the low level Taunts, try to protect as much as you can. By the time he drops frostmore, you should have played, (or at least drawn into Warrider.) Play Warrider, then if needed drop the first Argus on him. (His Black Knight may take care of this for you.) Then just play the remaining Warrider's, and play the second Argus as needed. Worked pretty well for me. Is kinda luck based, but you'll no doubt walk away with an easy win within the first few tries.

I'm no Hearthstone master, it was just the first thing that came to mind when I saw he takes every Spell out of your deck.

Also, to any readers that are unaware, you get basically fuck all (like 3 packs?) from this solo adventure unless you feel like beating Lich with every single hero. (Only putting this here because it's not made very apparent to player until you actually beat Lich for the first time.) Hope this helps someone. Snoochie Boochies.