Gently wring the bunches of lemon balm and mint to release the flavor. Place in a large glass pitcher, cover with the juices and the lemon slices. Chill overnight, occasionally stirring and pressing down on the herbs with the back of a wooden spoon.
Pour into iced glasses with a splash of sparkling water or champagne and a sprig of fresh lemon balm or mint.
Makes about 10 4-oz servings.