In a medium saucepan, combine the water and sugar and bring to a boil, stirring until the sugar is completely dissolved. Remove from the heat and let cool. Stir in the lemon juice. Pour the syrup into a 13-by-9-inch metal baking pan and freeze for at least 2 hours, stirring the granita with a fork every 20 minutes to give it a nice, granular consistency.
Meanwhile, in a medium saucepan, combine the water, sugar, rosemary, and cinnamon stick and bring to a boil. Simmer over moderately high heat for 10 minutes. Let cool completely, then strain into a medium bowl. Add the strawberries and let macerate for 1 hour.
Serve the granita in shallow bowls with the strawberries on the side.
The granita can be frozen for up to 3 days.
One Serving Calories 355 kcal, Total Fat .6 gm, Saturated Fat 0.