Combine sugar and water in a small saucepan over medium heat. Gently crush the rosemary leaves, to help them infuse the syrup. Add rosemary to the pot and let simmer for for 10 minutes, so that it thickens slightly and gets intensely rosemary-flavored. At the end of cooking, add the lemon juice, if using. I recommend the lemon juice if you plan on using the syrup for cocktails or spritzers. If you want to try to recreate the rosemary latte from Talula’s Table, leave it out.
Let syrup cool completely with the rosemary sprigs in the pot. When it’s cool, pour it into a small jar or bottle. If you’d like it to be more intensely rosemary-flavored, leave a sprig in the jar to continue the infusion.