To make the simple syrup, add the sugar and 1 cup of water to a pan over medium-high heat. Stir until the sugar is dissolved, and the liquid is coming to a boil. Remove from heat.
Combine the lemon juice, simple syrup, and 6 cups of water to a pitcher. Stir, and add extra lemon slices if desired. Chill in the fridge for up to 5 days, and stir before serving.