In a large bowl, combine ground lamb, grated onion, garlic, cumin, coriander, paprika, cayenne (if using), salt, pepper, and parsley. Mix well until fully combined.

Preheat your air fryer to 375°F (190°C), if needed. Form the lamb mixture into small patties or crumble it loosely. Place in the air fryer basket and cook for 10–12 minutes, flipping or shaking halfway through, until browned and fully cooked.

In a small bowl, stir together the Greek yogurt, lemon juice, olive oil, dried mint or dill, and a pinch of salt. Refrigerate until ready to serve.

While the lamb cooks, shred the lettuce, dice the tomatoes, and slice the red onion. Warm the flatbreads until soft and pliable.

Lay a flatbread on a plate. Add lettuce, tomatoes, red onion, and cooked lamb. Drizzle with yogurt sauce, wrap tightly, and serve warm.