In a medium saucepan over medium-high heat, combine sugar, water, and grated grapefruit zest. Stir continuously until the mixture comes to a boil, ensuring the sugar dissolves completely.

Remove the saucepan from heat and allow the syrup to cool for about 5 minutes.

Once cooled, stir in the freshly squeezed grapefruit juice and lemon juice into the syrup.

Pour the mixture through a fine-mesh sieve into a clean bowl to remove any solids.

Allow the strained mixture to cool completely at room temperature. Cover the bowl with plastic wrap and refrigerate for at least 4 hours.

After chilling, pour the grapefruit mixture into an ice cream machine and process according to the manufacturer’s instructions.

Transfer the freshly churned grapefruit sorbet into a tightly sealed airtight container and freeze for at least 2 hours to firm up.

When ready to serve, scoop the sorbet into chilled bowls or glasses and garnish with a sprig of mint or a thin slice of grapefruit.