Prepare a boiling water bath canner and 4 half pint jars. Wash new lids and rings in warm, soapy water and set aside.
In a medium saucepan, combine the apples, cranberries, and water. Set it over medium-high heat and simmer until the apples soften and the cranberries pop.
Once the fruit is tender, add the sugar, cinnamon, and lemon juice and zest.
Continue to simmer until you are pleased with the consistency. Know that it will thicken as it cools, keep that in mind.
Remove the compote from the stove. Use canning tongs to remove a hot jar from your prepared canner. Funnel the hot compote into the jar, leaving 1/2 inch headspace. Remove the air bubbles.
Wipe the rim, apply a clean, new lid and a ring and return the jar to the canner. Repeat this process with the remaining jars and compote. Process the sauce for 15 minutes, adjusting for altitude if you live above 1,000 feet in elevation.
When the processing time is up, turn off the heat, remove the lid from the pot and let the jars stand in the pot for an additional five minutes (this allows them to cool more gradually, which helps prevent siphoning and should also help develop a more robust seal).
Remove the jars from the canner and set them on a folded kitchen towel. Let them sit undisturbed for 12-24 hours so they can fully cool and seal. Before storing, make sure to check that the seals are firm and unbending. Sealed jars are shelf stable up to 18 months, any unsealed jars should be refrigerated and used promptly.