The Fume Knight is Raime, Vendrick's left hand. He and Velstadt, the King's right hand, had a falling out--you can read about it on The Rebel Greatshield I believe--and until the DLC, Raime was just a name and nothing more. Having him show up here answers a few questions about the game's overall lore.
I actually kind of like how the lore is sort of spotty, because it lets you fill in the blanks in your own ways. I have this whole idea of what drove Raime away, what clued Vendrick into Nashadra's true intentions, and who The Lost Sinner was all because there's just enough info for the stories to work, but not so much that you have to stretch and twist in order to avoid contradictions. Which is something Dark Souls III suffers a LOT from in my opinion.
Anyway, as Comic Sans said, there are enough wedges to finish off the Ashen Idols everywhere. Once you get the last one, you are officially done with this DLC.