Cut 4 lemons lengthwise into quarters, stopping 1 inch from bottom so lemons stay intact at base.
Working with 1 lemon at a time, hold lemon over medium bowl and pour 2 tablespoons salt into cavity of lemon. Gently rub cut surfaces of lemon together, then place in clean 1-quart jar. Repeat with remaining lemons and salt. Add any accumulated salt and juice in bowl to jar.
Pour 1 ½ cups lemon juice into jar and press gently to submerge lemons. (Add more lemon juice to jar, if needed, to cover lemons completely.) Cover jar tightly with lid and shake. Refrigerate lemons, shaking jar once per day for first 4 days to redistribute salt and juice. Let lemons cure in refrigerator until glossy and softened, 6 to 8 weeks. Preserved lemons can be refrigerated for up to 6 months.
To use, cut off desired amount of preserved lemon. Using knife, remove pulp and white pith from rind. Slice, chop, or mince rind and pulp as desired.
