Cook cranberries and apples in water until they are clear and tender. Press fruit through sieve to remove cranberry skins. Measure; there should be 3 cups of pulp. If you are slightly short, top off with some apple juice.
Add pineapple, sugar and lemon juice. Mix well and boil rapidly until the jam reaches its set point (approximately 222 degrees F.)
Test for the set point by placing a dollop of hot jam on a cooled plate and return it the freezer for a few minutes. Run your finger through the jam. If it wrinkles and doesn't fill back in, you have reached the set point. If not, return to heat and boil a couple minutes more.
Once the set point is reached, fill hot, sterilized half pint jars, leaving 1/4-inch headspace. Put on cap and screw on band hand-tight. Process in a boiling water bath for 10 minutes. Makes approximately 4 to 5 half-pint jars.
Notes
To substitute fresh pineapple, finely dice 1 1/2 cups pineapple. Combine in a blender with 1/2 cup pineapple juice or water. Pulse in blender to create crushed pineapple. Simmer pineapple and juice for 10 minutes to inactivate the enzymes in the pineapple.