FOR THE LEMON SIMPLE SYRUP:

With a vegetable peeler, peel the rind off one lemon, being careful not to get any pith.  Cut the rind into matchstick pieces.

In a small saucepan, combine 1 cup sugar and 1 cup water.  Over medium heat stir until the sugar has melted and the syrup is translucent.  At this point, add the lemon rind and cook until the rind is soft and bends like cooked pasta - about 3 minutes.  Remove from heat, taking out the rind and reserving it on a plate.

FOR THE LEMONADE:

In a large pitcher, combine 1 cup lemon simple syrup, lemon juice and water.  Stir.  Fill glass with ice and pour in lemonade.  Garnish with reserved lemon zest and a lemon slice.