Bring water to rolling boil.Add cranberries, heat until the berries “pop”.
Drain liquid and set aside. Cool completely.
Remove peels and seeds from fruit using a Foley Food Mill or colander.Discard peels and seeds.
Stir cranberry puree with liquid, heavy cream, sugar, and lemon juice.
Pour mixture into shallow 1-qt. freezer container. Cover and freeze until ice begins to form around the edges of container, about 1 hour; stir mixture. Freeze until slushy, stirring occasionally.
Scoop into individual serving bowls. Enjoy!