In a large bowl, toss the peeled, cored, and diced apples with the lemon juice. This will help prevent the apples from browning while you prepare the other ingredients. Set aside.
In a large dutch oven or heavy-bottomed saucepan, combine the granulated sugar, light brown sugar, cornstarch, ground cinnamon, ground nutmeg, and sea salt. Stir well to evenly distribute the cornstarch and spices among the sugars. Add 4 cups of water to the dry ingredients, and whisk until smooth. Bring to a low simmer over medium heat, stirring occasionally to prevent lumps or sticking.
Add the apples coated with lemon juice from Step 1 into the simmering syrup. Stir well to combine. Cover the pot and cook for 6-10 minutes, depending on the size of the apple pieces—smaller dice will cook faster. The apples should become fork-tender, and the sauce will thicken and reduce. Be sure to stir occasionally to prevent sticking. I like to pierce the apples with a fork to check for tenderness.
Remove the pot from heat and allow the apple pie filling to cool completely. Once cooled, it can be used immediately, canned, or frozen for later use. For a more vibrant flavor, I sometimes stir in a splash of fresh lemon juice at the end before storing.