Make a simple syrup by adding the sugar and water to a medium saucepan. Bring to a boil over low heat. Stir until the sugar dissolves, then remove from the heat and set aside to cool.
Add a gallon of cold water and the lemon juice to a large glass pitcher. Add the simple syrup and the lemon slices. Stir well. Pour the lemonade into tall glasses filled with ice. Garnish the rims with lemon wedges and enjoy icy cold!