In my instance Wyll doesn't act on the scene with Karlach after the MC leaves with Lae'zel. Karlach just monologues by herself and dies.
That's what happens if you play as someone who leaves the scene early: Lae'zel, Gith following Lae'zel or Spawn Astarion. The list used to include Gale, but they fixed it for him in December. Unfortunately they don't allow the scene with Wyll and Karlach play out on their own, which is stupid and I hope that it will get fixed eventually. That being said, what Ecc2ca wrote about Wyll having to be the Blade of Avernus is also true.
