Wash and quarter apples and plums. (No need to peel or core apples.) Place in a large pot and add 2 cups water. Cover and boil until apples are soft and the peels are falling off. Add sugar. Simmer another couple of minutes, until sugar is dissolved. Pour by small amounts into a food mill or other sieve, and press out the applesauce, discarding peels, seeds, and cores. Stir lemon juice, cinnamon, and nutmeg into applesauce.