Boil the water and sugar until the sugar has dissolved, then simmer for 3 minutes.
Divide the sugar solution into two portions. Simmer the lemon peel in one part for 10 minutes, then add the juice. In the other part, let the rosemary steep for 10 minutes over low heat. Pour the rosemary syrup into the lemon syrup through a sieve. Place in the cold place and set in the ice cream maker.