Grate the zest of the lemon and set aside. Juice the lemon into a small bowl. Rinse the cranberries. Drain well and put them in a non-metallic bowl with the sugar. Add the lemon juice and toss. Cover with plastic wrap, and leave on the counter overnight, turning once or twice.
Coarsely grate the apple and put it into a heavy based saucepan with the grated lemon zest. Strain in all the juice from the berries- scrape out all of the sugary stuff and add it to the pan. Add two big spoonfuls of berries, leaving the rest of the berries in the bowl for now. Add 1/2 cup of water and simmer 20 to 30 minutes, or until the apple is very soft and the mixture has thickened. Add the rest of the berries and heat through for 10 minutes.
Pour into sterilized jars. Seal tightly and turn upside down. Cover with a cloth and leave to cool completely before turning upright and storing in a cool place. The jam will keep for a couple of months, but once open it should be kept in the fridge and used up fairly quickly.
Notes
If you don't have superfine sugar in your pantry, swirl some regular granulated sugar in your food processor for about a minute to create superfine sugar).