Make the syrup by adding filtered water, sugar, and rosemary sprigs into a saucepan over medium heat. Bring to a low boil, then reduce to a simmer and allow to cook for about 10 minutes, whisking frequently, until the sugar is dissolved. Strain through a fine mesh sieve and set aside in the fridge to cool down.
Add your cooled rosemary syrup into the lemon / watermelon juice mixture, and then add your four cups of filtered water & stir well. Serve over ice with an extra lemon slice or fresh rosemary sprigs as a garnish.