Over medium high heat stir the water, sugar and rosemary until the sugar dissolves, about 5 minutes.
Remove from heat and stir in the lemon juice and the vodka. Cool to room temperature (about 2 hours.)
Strain through a fine mesh strainer into a bowl and refrigerate until thoroughly chilled.
Process in your ice cream maker per instructions.
Use fresh squeezed lemon juice, bottle lemon juice will not be good! Can use 1 tablespoon of dried oregano if you don't have fresh. Vodka is optional but helps keep the sorbet from freezing hard. If using vodka, my Raspberry Infused Vodka or Blueberry Vodka would make a lovely c