Mix chopped strawberries with ¼ sugar in a small bowl. Set aside.
Using an immersion blender puree chopped mango, 2 tablespoons sugar and 1 tablespoon lime juice until mixture is smooth. Pour into a 2 cup measuring cup. You should have 1½ cups (or more) mango puree.
Rinse immersion cup and puree strawberries with remaining 1 tablespoon of lime juice. Pour into a 1 cup measuring cup. You should have 1 cup of strawberry puree.
Layer popsicle molds beginning with mango puree, followed by strawberry puree, and ice cream. Continue to layer with fruit purees and ice cream leaving ¼-inch space from the top to allow for expansion. Using a chopstick or wooden skewer, lightly swirl the mixtures together. Place lid on mold and insert sticks. Freeze at least 8 hours or overnight. Run popsicle mold under warm water for easy removal.
Recipe by My Lilikoi Kitchen at https://www.mylilikoikitchen.com/2017/07/31/mango-strawberry-vanilla-ice-cream-popsicles/