Cut lemons lengthwise almost into quarters (leave attached at stem end). Pack as much kosher salt as you can (up to 2 tbsp.) into the cut center of 1 lemon and fit into a sterilized, bone-dry, widemouthed 1-qt. jar, cut side up. Repeat with remaining lemons and more salt (pack them in jar tightly).
Close jar and let sit overnight, then fill to brim with fresh lemon juice. Close jar and keep in a dark spot at room temperature 1 week, shaking once a day to redistribute salt and adding enough lemon juice to keep filled to brim. Let sit 3 more weeks before using.