The bridge still works with a knight pawn, as long as the attacker remembers to walk the king toward the centre, away from the edge, where there is room for the zigzag.
This is the Lucena with a g-pawn, mirrored from the usual textbook diagram. White's king is on g8 in front of the pawn on g7, the black king on e8 is cut off on the e-file, and Black's rook on h2 is ready to check from the h-file.