Make "simple syrup": Add sugar and water to a small saucepan and bring to a simmer. Stir frequently while the sugar is dissolving and remove from heat
Juice the lemons: While the water is heating for the simple syrup, juice the lemons. You need about 1 cup of lemon juice which should equal about 4 to 6 large lemons.
Crush the Rosemary: With the back of a spoon or a rolling pin, slightly crust the rosemary sprigs to release the most flavor.
Make the Lemonade: In the bottom of a pitcher, add the rosemary sprigs. Then combine the lemon juice, simple syrup, and water. Add 2 to 3 cups of additional cold water or as needed to achieve the taste you like. Taste add more water to dilute if necessary.
Chill: Refrigerate 30 to 40 minutes. Remove the rosemary leaves and transfer the lemonade to a serving pitcher; strain if necessary. Serve with ice, sliced lemons, limes (optional) and additional sprigs of rosemary.
Notes
Too Sweet?
If the lemonade is a little sweet for your taste, add a little more straight lemon juice to it.