Remove meat from the leftover turkey carcass and reserve for later dishes. Place turkey carcass (including all bones, cartilage, neck, and feet, if available) in a 7-quart stockpot or dutch oven with lid.
Pour apple cider vinegar and squeeze the lemon quarters over the carcass, then toss the rind in the pot. Add salt to the pot, then fill to the brim with water, stopping just short of the lip of the pot.
Bring the pot to a boil, skim and discard any frothy residue from the top. Reduce the heat to low or low-medium to bring the broth to a simmer, and cover. Allow the turkey bone broth to simmer for 24 hours, stirring occasionally. Periodically check on the broth to ensure the liquid is not evaporating too quickly, in which case drop the temperature and add a little more water to the pot. By the end of the 24-hour period, the liquid should be reduced by about half.
Once the liquid has slowly simmered and reduced by half, strain the turkey broth through a fine mesh strainer to separate the broth from the solids. Allow the strained turkey bone broth to cool at room temperature before placing in the fridge. Store in airtight containers until ready to use or freeze as needed.