1. Combine the sugar, water, and grapefruit zest in a medium saucepan, and bring to a boil over medium-high heat, stirring occasionally until the sugar dissolves. Remove the pan from the heat and set it aside to steep for 5 minutes.

2. Stir in the grapefruit juice and lemon juice. Strain the mixture through a fine-mesh sieve into a bowl. Stir in the black pepper, and set it aside to cool. (It will cool faster if you set the container in a bowl of ice water and stir it intermittently.)

3. Cover and refrigerate the sorbet base until it is thoroughly chilled, about 4 hours or up to overnight.

4. Process the sorbet in an ice cream machine according to the manufacturer's directions. Transfer it to a freezerproof container, cover, and freeze until ready to serve.