Labyrinth Minotaur doesn’t track the creature’s controller. If the affected creature changes controllers before its old controller’s next untap step, this ability will prevent it from being untapped during its new controller’s next untap step.

If the creature Labyrinth Minotaur blocked is untapped at the time its controller’s next untap step begins, this ability has no effect. It won’t apply at some later time when that creature is tapped.