Heat the glass quart-sized canning jars in the boiling water canner on medium-high with the lid on. Heat the lids in a small sauce pan of water on low with the lid on.
Check on the water and jars in the boiling water canner. When the water comes to a boil, place the lemons in the boiling water to cook for 3-5 minutes.
Remove the lemons from the boiling water with a slotted spoon and place them in a bowl of ice water. Allow the lemons to soak for 10-15 minutes to stop the cooking process.
While the lemons are cooling, combine the vinegar, water, and salt in a large non-aluminum stockpot to make the brine. Bring the mixture to a boil over medium heat.
Place 1 tablespoon of peppercorns in each quart-sized jar. Remove lemons from the ice water. Stand each lemon on end and slice a small X about halfway down. This will help the brine to permeate and preserve the lemon.
Arrange lemons and bay leaves (2 bay leaves to each jar) in jars. I was able to get 4 lemons in each jar, but I had to squeeze them in pretty tightly. You may be able to fit 4 lemons in as well. Use a spatula if needed to help release any air bubbles that may be trapped between the lemons.
Fill each jar with brine to the brim, covering the lemons completely. Wipe each rim with a cloth, place the lid on, and screw on the band tightly.
Using the tongs from the canning toolkit, if you have them, place each jar in the boiling water canner. Make sure the hot water covers the jars completely.
Process the jars for 15 minutes in a boiling water canner with the lid on.
Remove the hot jars with tongs and let cool completely. Store on a shelf or countertop away from direct light. Allow the jars to sit for at least six weeks to fully absorb the brine.