So the main theory surrounding the Old Iron King (associated with Gwyn) is that he's the prince of Alken or w/e. There's also the a lesser theory of his star-crossed lover, the princess of that other place, is the Lost Sinner (associated with the Witch of Izalith).
In any case, what I haven't seen suggested, as an explanation of why the Iron Keep sank into lava, is that it's directly connected to the Lost Sinner (who I would say is the princess) - the mistake being the what she suffers penance for (i.e., killing her lover). The actual act would be similar to what happened to Izalith, chaos fire and lots of lava. The origin of the Smelter Demon is inconsistent, with some making it seem it was another creation of the King, but the Smelter Sword says "the earth sprouted fire, and a beast arose from the flames". The king, while apparently killed, is transformed into a demonic monster, one I feel you could make a parallel to Ceaseless Discharge, despite his association with Gwyn (or maybe the 4 Kings or w/e they are actually aiming for). I've been reading a lot of lore, but I haven't seen any one make that sort of connection, despite believing what I said in the first sentence.
The Lost Sinner (Witch of Izalith) punishes herself for a grave mistake, her lover the Old Iron King is killed by a demon and his castle sinks into lava. Hmm... doesn't sound crazy to me!