This is the method most people use for preserving lemons. I’ve found references to it dating back to a British cookbook from 1808, although now most people associate it with Moroccan cooking. Only use unwaxed lemons for this method of pickling.
Slice the washed and dried lemons lengthwise, almost in quarters. You want the lemon to still be in one piece, but almost cut through. If the lemons have little nubs on the ends, cut them off before you almost-quarter the lemons.
Using pure sea salt, stuff the lemon. Pack it in well, and use about a tablespoon per lemon. Mush the lemon into a clean Mason jar; use quart jars. Repeat until you have the jar mostly full. Toss a little more salt on top.
Now you have several decisions to make. You can jam in some spices — I suggest some peppercorns, a couple cloves and a bay leaf. And you can choose to cover the lemons with vinegar or lemon juice, or not. Some people just keep mushing the lemons down until their own juice covers them. I cover them with lemon juice.
Wait at least 3 weeks before eating. I’ve kept these lemons for a year and they were fine. They will darken over time.