In a small saucepan, combine the sugar, lemon zest, star anise and water and bring to boil over high heat. Boil over medium heat for 5 minutes. Add the lemon juice and set aside to cool.
Strain the syrup into a bowl. Add the aquavit and place the bowl in the deep freezer. Take out and stir energetically with a fork every 30 minutes until completely frozen.
If the sorbet is frozen hard, let it soften briefly in the refrigerator before serving.