You'll need an ice-cream maker in order to make this refreshing chilled dessert.
Prepare an ice bath. In a medium saucepan, combine sugar, corn syrup, and 2 1/2 cups water; bring to a boil over medium-high heat. Cook until sugar completely dissolves, about 2 minutes. Remove from heat; add lemon juice. Pour mixture into a medium bowl; chill over the ice bath or overnight in the refrigerator.
Freeze mixture in an ice-cream maker, according to manufacturer's directions. Place in an airtight container in the freezer; store up to 1 month.