At the time the ability triggers, determine which creature Celestial Mantle is enchanting. As the ability resolves, determine who currently controls that creature (or, if it’s no longer on the battlefield, determine who controlled it when it left). That’s the player whose life total is doubled. It doesn’t matter who controls Celestial Mantle, who controlled the creature at the time the ability triggered, or what creature Celestial Mantle enchants at the time the ability resolves.