Chop the apples into bite-sized pieces, about ½ inch in size. Peel the apples first if desired. Add the chopped apples, granulated sugar, cornstarch, cinnamon, nutmeg, and lemon zest to a medium bowl. Toss until the apples are evenly coated.
In a separate bowl, stir together the oats, flour, sugar, cinnamon, nutmeg, and salt. Pour the melted butter over the oat mixture. Mix with a fork until crumbly and small clumps form.
Divide the apple mixture evenly between 4 small ramekins. You can also use one 6-inch round baking dish that fits inside your air fryer. Gently press down the apples so they're relatively compact.
Sprinkle the crisp topping evenly over the apples. Leave the topping loose rather than packing it down.
Place the ramekins or baking dish in the air fryer basket. Air fry at 375°F for 15 minutes, or until the topping is golden brown and the apple filling is bubbling around the edges.
Test an apple with a fork. If the apples are still too firm, continue cooking for another 2-3 minutes. Remove from the air fryer and let cool for about 5 minutes before serving.