Combine sugar and water in a small saucepan, stirring well. Bring mixture to a boil; cook, stirring constantly, 1 minute or until sugar dissolves. Let cool slightly.
Position knife blade in food processor bowl; add watermelon, sugar mixture, and lemon juice. Process until smooth. Pour mixture into an 8-inch square pan. Cover and freeze at least 8 hours or until firm.
Position knife blade in food processor bowl; add frozen watermelon mixture. Process until smooth but not thawed. To serve, scoop into 2 dessert dishes, and serve immediately. If desired, garnish with blackberries and watermelon wedges.