Scrub lemons and dry well. Quarter lemons lengthwise, leaving 1/2 inch at bottom intact. Toss fruit with salt and transfer to a sterile 4-cup glass jar. Use a wooden spoon to press lemons to fit. Add lemon juice and any remaining salt. Seal jar tightly and shake to combine. Let stand at room temperature for 3 days, shaking jar each day. Transfer to refrigerator for 3 weeks until rinds are soft. Rinse before using. Try them in salads or stews, or whisk the pulp into a salad dressing or a Bloody Mary.
Preserved lemons can be refrigerated for at least 3 months.