Wash the apples and cut them into eighths, then remove the seeds and cut away the stem and a little of the core (not a lot, the pectin in the core is needed for thickening).
Put the apples in a heavy saucepan and add enough water to cover the bottom. Cover and heat on high until apples are steaming, then reduce heat to medium or medium-high and cook, stirring occasionally, until apples are puffy and soft, about 45 minutes.
Put apples into a food mill and push them through (a cone-shaped sieve and wooden pestle also work), leaving skins. Add lemon juice and sugar. Serve with a little cinnamon sprinkled on top.