Slice half of the lemons from top to bottom into quarters, but don't cut all the way through so that the lemon has four "petals." In a mixing bowl, toss the cut lemons generously with salt, packing some inside each lemon. Place the salted lemons into the quart jar. Juice the remaining lemons and pour the juice into the jar. Fill the jar to the top. Secure the lid and let sit in a cool dry place for at least 3 days. The lemons can set longer and will keep in the refrigerator. I keep mine for a very long time so I cover the whole thing with some olive oil. You don't have to make so many, you can just do a couple, once you have them covered in salt then just put in lemon juice to cover. Also note that if you are using a canning jar and a canning flat as a lid, you should cover the jar mouth with plastic wrap before putting the lid on to avoid corrosion of the lid.
To use, remove a quarter lemon and pull out the pulp. I usually put the pulp back in the jar to keep the volume of liquid up. Dice or thinly slice the peel. These can be used in chicken stew, even dice up the peel and put a little in tuna salad. I make ahi tartare (minced fresh raw tuna) and add some to that along with my other seasonings. And of course in that carrot salad. Any time you have a savory dish that calls for lemon zest or juice and has salt, you can use some of this for an interestingly different flavor.