Using a sharp knife, cut each lemon lengthwise almost through to the stem end, and then rotate the lemon 45 degrees and cut so that the lemon is almost quartered; the lemon should still be connected at one end, but you should be able to open it up, much like a flower. Spoon 1 tablespoon of the salt into the center of each lemon and press to close. Squeeze the 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 the lemons to the jar. Cover the jar and set aside in a cool, dark place for several days.

Uncover the jar and press down on the lemons with your fingers or the back of a spoon. Add enough lemon juice to cover them completely -- the amount of juice will vary depending on their ripeness (I have had batches where no additional lemon juice was necessary because the lemons themselves exuded so much juice). Close the jar and once again set aside in a cool, dark place for 1 month, shaking the jar occasionally to distribute the salt and brine. 

When the lemons are ready, the peel and flesh will be very soft and you will see that the flesh easily peels away. Discard the flesh, rinse the peel briefly under cool water, and use as needed.