Rinse and quarter the medlars, and put them in a large pot – skins, seeds, and all. Chop up the apple and add, with the seeds and core, as well. Then add the lemon half to the pot, and pour in enough water so that the medlars are floating in liquid, about 2 quarts (2l).
Cook the mixture until it begins to boil, then reduce the heat and let it cook at a low boil for 45 minutes.
Line a colander with several layers of cheesecloth or gauze, set it over a deep bowl, and ladle the cooked medlars and the liquid into the colander. Let it strain overnight undisturbed. Do not press down on the cooked fruit to extract more juice from it or your jelly will be cloudy. (It’s very tempting, but resist.)
The next day pour the liquid into a large pot – you should have about 1 quart (1l). Put a small plate in the freezer. Add the sugar to the juice in the pot and cook the jelly until it reaches 220ºF (104ºC) or until it jells, which may happen a little before or after that temperature. To test the jelly, put a spoonful on the plate in the freezer and let chill a few minutes. If, once cold, it wrinkles when you push it with your finger, it’s done. If not, continue to cook the jelly until it jells. When ready, if you wish, you can offset sweetness with a few drops of fresh lemon juice.
Ladle the jelly into clean jars.