Toss the apples with lemon juice and set aside. Combine the sugars, cornstarch, cinnamon, nutmeg, and salt in a saucepan. Stir in water. Bring mixture to a boil. Boil 2 minutes stirring constantly.
Add the apples and bring to a boil again. Reduce the heat to medium low and simmer for 10-12 minutes. Cool completely. It will set up as it cools. Makes 4 cups of apple pie filling. Keep refrigerated in a sealed container for 4-5 days.