In a medium saucepan over medium-high heat, bring the sugar, water, and grapefruit zest to a boil, stirring occasionally until the sugar dissolves. Remove the pan from the heat and let it cool for 5 minutes.

Stir in the grapefruit and lemon juices. Strain the mixture through a fine-mesh sieve into a bowl and set it aside to cool. Cover and refrigerate the sorbet base until it is thoroughly chilled, at least 4 hours.

Using an ice cream machine, process the sorbet according to the manufacturer’s directions. Transfer it to a tightly sealed container, and freeze until ready to serve. Enjoy!