1. Preheat grill to 350°F (175°C) or prepare a campfire with steady embers.
2. In a large bowl, toss the peeled, cored, and sliced apples with lemon juice, cinnamon, cornstarch, salt, granulated sugar, and brown sugar until evenly coated.
3. In a separate bowl, combine the oats, flour, brown sugar, cinnamon, and nutmeg. Cut in the melted butter until the mixture becomes crumbly.
4. Lay out six pieces of heavy-duty foil approximately 12×12 inches. Distribute the apple mixture evenly in the center of each foil square.
5. Generously sprinkle the crumb topping over the apples.
6. Fold and seal the foil packets, allowing some space for heat circulation.
7. Place the foil packets on the grill rack or hot embers away from direct flames. Cook for about 15-30 minutes, checking for doneness at 15-20 minutes until apples are tender and topping is golden brown.
8. Remove from heat and carefully let packets cool slightly before opening.
9. Serve warm directly from the foil packets with optional toppings like vanilla ice cream, caramel sauce, or whipped cream.