Remove the lemon peel with a vegetable peeler or a pairing knife, avoiding to remove the white pith which is bitter. Transfer the peels in a 1 gallon glass jar. Pour in alcohol, stir, close tightly and place the jar in a cool, dark place, undisturbed, for 5 weeks.
Juice the skinless lemons and pour the liquid into an ice cube tray (volume of each cavity is 1 tbsp.). Transfer to the freezer until solid. Transfer lemon cubes in a re-sealable plastic freezer bag until needed for a recipe that calls for 1 tablespoons lemon juice.
When the 35 days are up, place cheese cloth at the bottom and the sides of a colander; place colander over a large pot. Pour in the alcohol and peels into the lined colander; drain well. Carefully remove the cheese cloth and discard the peels.
Transfer the pot on a stove and add sugar with distilled water. On medium-high, stir mixture until sugar is dissolved. Just before the limoncello starts boiling, remove from the heat to cool off. Pour liqueur into sterilized bottles, close lids, wipe out and let them sit for 7 to 10 days before serving. Makes 2 ¾ liters.