To make a simple syrup, combine sugar and ½ cup water in a small pot. Bring to a boil. Stir, and reduce heat to medium-high. Stir occasionally until sugar is dissolved, approximately 5 minutes. Let the simple syrup cool.
Finely chop the basil.
Add the basil, 4 cups of water, lemon juice, and ¼ cup of the simple syrup to a pitcher. Stir well, and chill.