Peel, core, and dice the apples into small pieces (1/4 inch or about 1/2 cm cubes).
Toss the apples first in lemon juice and then the sugar. Stir, so they're evenly coated. Cover and set aside to macerate for at least 2 hours, or overnight.
After maceration, place the apple mixture and cranberries into a jam pot. (If canning, prepare a water bath canner before turning on the jam to start cooking.)
Turn on the stove to medium-high heat and cook the apple-cranberry mixture until it thickens. (About 6 to 10 minutes.) Stop when it's not quite as thick as you want the finished jam, as it thickens considerably when it's cooling. It's done when the cranberries have popped and fallen apart, but the apple chunks are still pretty much in their original shape.
Remove the jam pot from the heat and ladle into prepared jars, leaving 1/4 inch headspace.
If canning, process in a water bath canner for 10 minutes (15 minutes above 6,000 feet in elevation).
Cool jars completely on a towel on the counter, and check seals. Store any unsealed jars in the refrigerator for immediate use. Sealed jars will keep on the pantry shelf. Refrigerate after opening.