In a large saucepan, combine the sugar, 1 cup water and lemon zest. Cook and stir over medium heat until sugar is dissolved, about 4 minutes. Remove from the heat. Stir in lemon juice and remaining water. Pour into a 2-qt. pitcher; refrigerate until chilled.
Stir in rum. For each serving, place 3/4 to 1 cup ice in a Collins or highball glass. Pour lemonade mixture into glass. Garnish with lemon slices as desired.