Trim the ends off the lemons. Slice each lemon into 8 wedges, removing any seeds as you go. Reserve as much of the juice as possible.
Layer the lemon wedges in a wide-mouthed 16-ounce canning jar, covering each layer with salt. Pack the jar as tightly as possible, pressing down to release the lemons' juice as you go and leaving about 1/4 inch of headspace in the jar.
Cover the wedges with the reserved lemon juice from the cutting board and the ends. If your lemons do not release a significant amount of juice, top off the jar with the juice of another lemon.
Stash in the refrigerator for 4 days, then flip the jar over and age another 4 days before sampling. The peel should be nice and soft. Rinse before using.
Expect peak flavor and texture after about a month. As long as they're kept refrigerated, preserved lemons should keep indefinitely.