Add the autumn olive berries, water and chopped apple (peels on), if using, to a large pot on medium heat. Stir frequently, smooshing berries for about 15 minutes until the fruit softens.
Press the hot fruit mixture through a metal sieve or food mill to remove the seeds. Heat the resulting juicey pulp with the sugar and lemon juice over medium, stirring frequently and skimming off any foam.
If you can run your finger through the jam and leave a clean line - slow to fold in on itself, then it’s done. Let the mixture cool, continuing to stir to prevent separation. Add a little squeeze of lemon juice to each jar and pour in jam, leaving a little bit of head space. Cover with sterilized lids and if planning to use quickly, turn upside down to cool and store in fridge or for long term storage, process in a boiling water bath for 15 minutes.
