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Predictions:
Billy will have passed. Maybe because of the Lich King, maybe he just passed, the point being Finn has to finish what he started.
The Lich King will kill/be believed to have killed Princess Bubblegum. By the end of the episode she will be revealed to have survived/been brought back to life.
The Lich King himself will survive the encounter, whose return will be a lingering threat in the next season.