If I remember mine correctly, the Lich King itself is a single piece. No feet - just billowing robes at the bottom of the model that sweep forward rather than straight down. I seem to recall that there's a small metal peg to slot into the base, so you could drill a hole in the new tiled base. Alternatively, file a flat spot onto the base of the robes and maybe pin the model to the new base.
The complete model has a metal base with space for the King and the separate skeleton warrion. Can't remember how many pieces the skeleton comes in (the shield may be separate), but I do remember that it's easy to remove all the clods of earth from him. You could make a separate "rising from the grave" base for him with some basing gel/greenstuff/milliput and a gravestone in about 5 minutes.
There may be lumps of earth on the Lich King's robes as well - they were easy to remove too!
I mounted the whole scene onto a blank plastic 50x50mm base, built up the edges with Vallejo pumice gel to blend in with the metal base and removed all the lumps of earth. And snipped off the tines of his crown. It's a nice model.