Combine 1 cup sugar and water in a medium saucepan, stirring until sugar dissolves; bring to a boil. Cook 5 minutes. Pour sugar mixture into a medium bowl; stir in lime rind and next 4 ingredients (through orange juice).
Place strawberries in a food processor; process until smooth. Add strawberry puree to sugar mixture; stir well. Cover and refrigerate for 3 hours or until chilled.
Pour strawberry mixture into the freezer can of an ice-cream freezer, and freeze according to the manufacturer's instructions. Spoon the mixture into a freezer-safe container; cover and freeze for 8 hours or until almost firm.