Try to find ruby-red or star-ruby grapefruit, since their dark-pink flesh makes the most beautiful juice.
Prepare an ice bath. Combine the sugar and 2 cups water in a medium saucepan. Stir well, and set over medium-high heat. Bring to a boil, and cook, stirring occasionally, until all of the sugar has dissolved, about 10 minutes.
Pour the sugar syrup into a medium bowl, and set bowl in the ice bath to cool; the syrup should yield 2 1/2 cups.
When ready to serve beverage, combine the lemon juice, grapefruit juice, and the sugar syrup in a medium pitcher. Add the lemon rounds, and fill with ice cubes.