This sorbet is delicious with bits of lime zest throughout, but if you'd rather have a perfectly smooth version, strain the mixture before freezing. Cocktail Party Recipes
Place the lime in a colander and pour about 1 cup of boiling water over it to remove any wax or spray; pat dry. Using a vegetable peeler, remove the zest, making sure to scrape off any white pith that clings. Mince the zest (there will be about 2 teaspoons). Squeeze out 1 tablespoon of juice from the lime; reserve.
Place the zest and sugar in a small bowl and using a wooden spoon, crush them until well combined, about 3 minutes. Set aside for 30 minutes.
Transfer the sugar/zest mixture to a deep pitcher or bowl. Stir in the gin and reserved lime juice. Slowly pour in the tonic water and stir to dissolve the sugar. Refrigerate, covered, until chilled, about 30 minutes. Strain if desired.
Pour the mixture into an ice cream maker and freeze according to the manufacturer's instructions. Turn into a chilled bowl, cover and freeze, or serve at once.