Place the peeled, cored, and quartered apples into a large pot. Add the strips of lemon peel, the lemon juice (or vinegar), cinnamon, water and salt.
Bring to a boil on high heat, then lower the temperature. Cover the pot, and maintain a low simmer for 15 to 20 minutes, until the apples are completely tender and cooked through.
Once the apples are cooked through, remove the pot from the heat. Remove the lemon peels.
Use a potato masher to mash the cooked apples in the pot to make a chunky applesauce. For a smoother applesauce, you can either run the cooked apples through a food mill or purée them using an immersion or stand blender.
Adjust the seasoning and consistency as needed. If the applesauce is too thick, add more water to thin it out.