Bring 1 cup (250ml) water to a boil in a saucepan. Stir the sugar and basil into the water and return to a boil; cook at a boil for 10 minutes and immediately remove from heat. Chill in refrigerator until slightly cooled, about 10 minutes.
Blend the blueberries, 1/2 cup (125ml) water and the lemon juice in a blender until smooth; pour into a pitcher. Remove the basil leaves from the simple-syrup mixture; discard the basil. Stir the syrup into the blueberry mixture. Add the carbonated water to the mixture and stir gently.