Zest 1 lemon using a vegetable peeler, and place peel into a small saucepan. Add basil, sugar and ¾ cup water. Bring to a boil, stirring until sugar is dissolved. Remove from heat and let steep for 10 minutes.

Strain basil syrup mixture (discard basil and peel), and refrigerate until cool.

Juice all lemons into a pitcher, add 6 cups cold water, and basil syrup.