!To make the Simple Syrup:
In a saucepan, cook water and sugar over medium heat until the sugar is completely dissolved and the mixture is a clear syrup. Set aside.
To a pitcher, add lemon juice, simple syrup, and cold water. Stir and taste. If too sweet (every batch is different according to your lemons), add more cold water until desired sweetness is reached. Add basil, lemon rounds and ice just before serving. Stir and serve.