In a small saucepan, combine 1 cup sugar, 1 cup water, and 3-4 sprigs or fresh rosemary. Bring to a boil, then reduce heat and let it simmer for 5 minutes to let the rosemary flavor infuse.
Carefully strain out the cooked rosemary through a sieve, collecting the syrup in a heat-safe container. Or use a slotted spoon to remove the rosemary. You should have a little over 1 cup of rosemary simple syrup.
In a large pitcher or bowl, combine 1 cup lemon juice, 1 cup rosemary syrup (you'll have a few tablespoons left over), and 3 cups cold water. Stir well, give it a taste and adjust with more lemon juice, syrup, or water, depending on whether it's too sweet, too sour, or too concentrated.
Pour over ice to serve, or chill in the fridge until ready to serve.