Combine sugar and water in a medium saucepan. Bring to a boil over high heat; cook 1 minute. Remove from heat; cool 1 hour. Stir in lime juice; set syrup aside.
Place strawberries in a food processor; process until smooth. Stir in half of syrup. Pour strawberry mixture into an 8-inch square glass dish. Rinse processor bowl; wipe dry. Add kiwifruit; process until smooth. Stir in remaining syrup.
Use a measuring cup to drizzle kiwi mixture in a swirl pattern over the strawberry mixture. Cover and freeze 8 hours.
Shortcut Kitchen Tip
To easily create a swirl pattern, pour the red strawberry mixture into an 8-inch square glass dish. Then scoop the green kiwi mixture into a measuring cup, and slowly drizzle it in a swirl pattern over the strawberry mixture.
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