In a medium saucepan, combine cranberries, sugar, and water. Bring to a boil over medium-high heat, then reduce heat and simmer for 10 minutes, or until cranberries have popped and softened.

Carefully transfer the mixture to a blender or food processor. Blend until completely smooth.

Strain the purée through a fine mesh sieve into a bowl to remove skins and seeds, pressing with a spoon to extract all the juice.

Stir in the orange juice and lemon juice until well combined.

Pour the mixture into a freezer-safe container and freeze for at least 4 hours or until firm.

To serve, let sit at room temperature for 5-10 minutes to soften slightly. Scoop and serve chilled.