Only the player who controls the enchanted creature can activate the ability it gains from Lunarch Mantle. This might not be the controller of Lunarch Mantle.

You can activate the ability Lunarch Mantle grants to your enchanted creature by sacrificing any permanent you control, including Lunarch Mantle or the enchanted creature itself. If you sacrifice Lunarch Mantle this way, the creature it previously enchanted still gains flying.