Using a sharp knife, cut each lemon lengthwise almost through to the stem end, and then rotate the lemon 45 degrees and repeat; the lemon should still be connected at one end but you should be able to open the lemon up much like a flower.
Spoon 1 tablespoon salt into the center of each lemon and press to close. Squeeze lemons into a sterilized jar with a tight-fitting lid (it's ok if you need to squeeze firmly to compact the lemons; they will soften over time) and add any salt that has fallen from lemons to the jar. Cover jar and set aside in a cool, dark place for several days.
Uncover jar and squeeze downward using your fingers or the back of a spoon to compress lemons. Add enough lemon juice to completely cover lemons -- the amount of lemon juice will vary depending on the ripeness of the lemons (I have had batches where no additional lemon juice was necessary because the lemons themselves exuded so much juice). Cover jar and set aside in a cool, dark place for 1 month, shaking jar occasionally to distribute salt and brine.
When lemons are ready, the peel and flesh will be very soft. The peel is the most often used portion -- you will see that the flesh easily peels away. Discard flesh and then rinse peel briefly under cool water; use as needed.
Cook's Note: If you happen to have access to homegrown lemons, this is the perfect unique way to preserve their fresh flavor. Any variety of lemon will work as long as the lemons have not been waxed. Keep in mind that these lemons need to sit for at least 4 weeks before using, so make a batch when lemons are in season and use them throughout the year -- they will keep for up to one year after mature and the flavor will improve with age.