Yours. "Holder's" there refers to the holder of Consumed by Wants, not the Lost Soul, and you are still the holder since nothing relinquishes control of Consumed by Wants.
However, if you do put it on your opponent's Lost Soul, they have the option to surrender that Lost Soul in a rescue attempt, which would result in Consumed by Wants being discarded so it wouldn't follow the Lost Soul to a Land of Redemption.
