Remove the tags from the tea bags and tie them all together. (My mom taught me this trick.)
Boil 2 quarts water in a kettle or a pot. When boiling, remove from the heat and add the tea bags and the fresh mint leaves. Cover and allow to steep for at least 20 minutes. If you have the time, let it steep for up to an hour. The longer the tea bags and mint can steep, the better. Duh.
While your tea is steeping, heat sugar and fresh lemon juice until the sugar dissolves and the liquid becomes clear. Set aside.
Once the tea is steeped, strain it into a large pitcher, discarding the mint and tea bags. Mix in the lemon simple syrup and refrigerate until cool.
When your iced tea is cool, add some fresh mint and lemon slices to the pitcher if you like. You can now pour the rum into the pitcher OR you can add rum to individual cocktails. Serve your iced tea over ice. Garnish with a lemon slice or two and a sprig of fresh mint for flair.