If giving as gifts, let recipients know to rinse lemons well before using (to remove excess salt) and to use only the rinds.
Sterilize two 1.5-liter canning jars and two 1-liter canning jars with clamp-top lids (we used Fido brand) by boiling them and their rubber seals in water 10 minutes. Remove with tongs, and let cool.
Cut stem end off each of 24 to 30 lemons. Make 5 or 6 slits (a little less than 1/2 inch deep) down the length of each lemon with a sharp paring knife, cutting to within 1/2 inch of bottom of lemon but not all the way through. Press top of lemon with your palm to flatten and cause slits to splay open. Gather and save any juices that accumulate on cutting board. Pack as much salt as possible (about 1 tablespoon) into each slit.
Place about 1/2 cup salt in each 1.5-liter jar, and pour in a little lemon juice. Working with 1 jar at a time, add 1 lemon, and flatten as much as possible. Sprinkle in a little more salt, add another lemon and repeat process, adding more juice every so often. Repeat until you reach top of jar (each jar should take 12 to 15 lemons). Seal jars, and refrigerate 20 days, shaking and rotating once a day, before giving as a gift. Most but not all of the salt will dissolve.
For remaining lemons, trim stem end of each lemon and cut in half lengthwise; cut each half into 8 pieces. For every 2 cups of lemon pieces, toss with 1/2 cup salt in a bowl. Fill two 1-liter jars with lemon mixture, pressing down as many lemon pieces as possible and causing them to exude some of their juice. Seal jars, and refrigerate at least 10 days, shaking and rotating once a day, before giving as gifts.