Combine the water and sugar in a small saucepan and bring it to a simmer over a medium flame. Stir until all the sugar is dissolved. Allow the syrup to cool, then chill it for at least 1 hour.
Combine the syrup with the grapefruit juice, 1 teaspoon of grenadine, 4 tablespoons of lemon juice, and the Pernod. Taste. Now add more lemon juice if needed—this will depend on the acidity of all the fruit. Remember, this sorbet should not be too sweet. Add more grenadine if you want it to be pinker.
Chill the mixture for 2 hours, then freeze it in an ice cream maker, according to manufacturer's instructions.
Recipe courtesy of Anna Thomas, The New Vegetarian Epicure, Knopf, 1996