Wash a 24-ounce jar and its lid in soapy water and dry well. Using a sharp knife, cut an X shape into each lemon so it is quartered but not cut all the way through; it should look like an open flower that can be closed with the palm of your hand. 

Working over a bowl, hold one of the lemons in your hand. Pack the salt inside, close it, and fit it into the bottom of the jar. 

Keep working with the lemons and the salt, fitting the lemons in as tightly as possible. Sprinkle more salt on the lemons as you go along. 

Juice will start to gush out of the lemons and fill the glass with liquid as you move your way up; this is what you want. 

Continue salting and packing the lemons until the jar is filled almost to the top with lemons and lemon juice. If you need to, add lemon juice to cover and fill the jar. 

Seal tightly, place the jar on a plate to catch leaks, and leave out in a sunny place for at least 2 weeks and up to 3 months, flipping the jar occasionally so the salt and lemon juice move around a bit. 

Transfer to the refrigerator, where the preserved lemons will last for up to 1 year.