Remove the stems and cut off the tips off the lemons. Cut each lemon lengthwise into quarters, but not cut all the way through – you want to leave them attached at the base (or fully quarter them if you wish).
Pack the cut sides with lots of salt, close the lemons and place them in a jar. Compress the lemons as you add them to the jar to release some of their juices.
When the jar is nearly full (or as full as you’d like), squeeze in fresh lemon juice to almost cover and top with a generous sprinkling of the salt. Cover the lemons, and set aside in a cool, dark place. A cupboard or food pantry is fine.
Every two or three days, open the jar and compress the lemons to release more juices. Do this for the first week, or until the lemons are submerged in juice.
The lemons will be pickled and ready to use in about four to five weeks, once the rinds are very soft. You can continue to preserve them longer if you like. Once opened, transfer the jar to the refrigerator, where they should keep well for several months.