In a bowl, combine mayonnaise, ketchup, sweet pickle relish, sugar, vinegar, and salt. Adjust to taste and set aside.
Preheat your air fryer to 180°C (360°F).
Divide the ground beef into 4 equal portions and shape into patties. Season both sides with salt and pepper.
Place the patties in the air fryer basket. Cook for 8-10 minutes, flipping halfway through, or until they reach your desired doneness.
In the last minute of cooking, top each patty with a slice of American cheese to melt.
Lay out the tortillas and spread each one with the prepared In-N-Out style sauce.
On each tortilla, layer lettuce, tomato slices, pickles, and cooked onions.
Place a cheese-topped patty on top of each tortilla.
Carefully fold the tortilla, tucking in the edges to form a tight wrap.
Place the wraps in the air fryer basket (may need to be done in batches). Air fry at 180°C (360°F) for 2-3 minutes per side, or until the tortillas are crispy and golden brown.