To Make the Salted Lemons: Wash and dry the Meyer lemons in a colander, then transfer to a large mixing bowl. Add the coarse salt.
Using your hands, rub the sea salt against the lemons. The coarse salt will act as a gentle abrasive on the lemons, removing the bitter essential oils from the skin. Scrub the lemons 30 minutes. At the end, the salt should take on a faint yellow tinge, indicating that the essential oils have been extracted from the lemon peels.
Transfer lemons to a colander. Rinse under running water and rub away any large salt granules, then transfer them to a large bowl of clean water. Set the lemons aside 10 minutes to remove any residual salt, then place them back into the colander and set them aside to dry completely.
While the lemons are drying, prepare a brine: Combine the Red Boat Salt and 3⁄4 cup water in a pot. Bring the brine to a boil, then remove the pot from the heat. Let the brine cool completely. Once the brine is cool, stir in a pinch of citric acid, if using.
Once the lemons are dry, pack them into a quart jar. Add the minced chiles and, optionally, the licorice root.
Pour the cooled brine into the jar. Place a tiny dish or ramekin inside the jar to keep the lemons submerged in the brine.
Cover and set aside in a cool place for at least 3 months before using.
To Mix the Cocktails: Add salted lemons, along with their juices, to a large glass. Add the sugar.
Use a pestle or spoon to muddle the lemon and sugar until the sugar dissolves.
Add vodka, ice cubes, and club soda. Stir to combine. Serve immediately.