Whisk together the pomegranate juice, lime juice and powdered sugar until sugar is dissolved. Add cream and whisk (either by hand or with a hand mixer) until soft pink peaks appear.
Spoon ice cream into a plastic or glass container with a snug-fitting lid, smooth it down to compact it and freeze for at least 4 hours or overnight.
Serve with fresh pomegranate seeds as a garnish, if desired.