The night before or several hours prior to serving bruise the bunches of lemon balm and mint between your hands to release flavor. Place them in a large crock or pitcher, and cover with the juices and lemon slices. Chill thoroughly. If possible stir while pressing down on herbs with back of a wooden spoon.
Remove the herbs (they will have discolored) squeezing them and replace with a few fresh herb sprigs.
Pour punch into iced glasses with lime slices, and a sprig of fresh lemon balm or mint.