Combine cranberry juice and sugar in a medium saucepan. Cook over medium heat 3 minutes or just until sugar dissolves, stirring once. Place pan in a large ice-filled bowl; cool completely, stirring occasionally.
Stir in lemon juice and sparkling water. Pour mixture into a 13 x 9-inch glass or ceramic baking dish. Cover and freeze until firm (about 2 hours). Remove mixture from freezer; scrape entire mixture with a fork until fluffy.