Place watermelon, strawberries, and 1 tablespoon of lime juice in a blender and puree until completely smooth. Pour mixture into popsicle molds, filling only 2/3 of the way. Secure the lid to the mold and insert popsicle sticks. Freeze for 3 to 4 hours or until solid.

While popsicles are freezing prepare the kiwi mixture. Cut each kiwi in half and scoop out flesh with a spoon. Place kiwi in blender and add remaining lime juice. Puree until smooth. After 3 to 4 hours, remove popsicles from freezer and remove the lid. Fill the last remaining space with the kiwi mixture. Secure the lid to the popsicle molds and return to the freezer. Freeze until completely frozen, approximately another 3 to 4 hours.