Scrub the lemons well. Peel the rind thinly, avoiding the white pithe, and set aside the lemons.
Place the lemon rind, lemon balm leaves, and the sugar into a small heat-proof pitcher. Pour the boiling water into the pitcher and stir well, crushing the lemon balm leaves to release their flavor. Leave mixture to infuse for about 15 minutes.
Now, cut the lemons in half and squeeze out the juice. Strain juice into a large glass pitcher, add a few fresh sprigs of lemon balm, and add the cooled, strained syrup. Top up with water or half-water half-ice, and chill until needed.