Begin by thoroughly cleaning the lemons. Carefully peel the skin off the lemons, making sure to avoid including any of the bitter white pith. Reserve the peeled lemons for later use.

In a small, heat-resistant jug, combine the thin lemon peels, fresh lemon balm leaves, and sugar. Pour the freshly boiled water over these ingredients. Stir the mixture vigorously, pressing against the lemon balm leaves to better extract their aromatic oils. Allow this blend to steep and infuse for approximately 15 minutes, releasing all the flavors.

Meanwhile, halve the reserved lemons and juice them, ensuring to strain the juice to remove any seeds or pulp. Transfer this fresh lemon juice into a large pitcher. Add a few sprigs of lemon balm to enhance the aroma.

Once the infused syrup has cooled, strain it and pour it into the pitcher with the lemon juice. Dilute the concentrated mixture with plain water, or a mix of water and ice, according to your preference. Stir well.

Place the pitcher in the refrigerator to chill. Serve the refreshing lemon balm beverage in glasses, possibly over more ice, and garnish with sprigs of lemon balm to beautify and add a touch of freshness.