In a large heavy-bottom pot, add the apples, water and lemon juice. Cover and turn heat to medium-high. Bring to a simmer and cook until the apples start to release some liquid, about 10 minutes. Remove the lid and stir.
Reduce the heat to medium-low and cook covered for about 45 minutes, stirring occasionally. While stirring, you can mash some of the apples with a fork or potato masher. The apples should be very soft.
Let cool for about 30 minutes.
Transfer the apples, in batches, to the food mill fitted with the medium disk placed over a bowl, and process the apples through the food mill. Every once in a while, reverse the dial on the food mill to scrape the skin off the bottom, process again and then discard the solids as you go.
If the sauce is watery, return it to the pot and simmer over medium heat until thickened.
Taste the applesauce for flavour. Add cinnamon, salt and sugar if desired (I generally never add sugar).
