In a small saucepan, bring sugar and water to a boil. Cook and stir until sugar is dissolved; set aside to cool.
Place mangoes and strawberries in a food processor; add sugar syrup and lime juice. Cover and process until pureed. Transfer puree to a 13x9-in. dish. Freeze 45 minutes or until edges begin to firm. Stir and return to freezer. Freeze 2 hours longer or until firm.
Just before serving, transfer to a food processor; cover and process 2-3 minutes or until smooth