In a medium saucepan combine granulated sugar and water. Bring to a simmer and cook until sugar is dissolved. Remove from heat and add mint sprigs. Stir until it wilts and is covered by the sugar water mixture. Cover the pan and allow to sit for 20 minutes. Strain mint leaves out of syrup and refrigerate until cold.
Meanwhile, combine lemon juice and water in a pitcher. Stir in chilled mint simple syrup. Add lots of ice, lemon slices and mint then serve.
