Prepare the tzatziki sauce by combining yogurt, olive oil, cucumber, mint, dill, lemon zest, lemon juice, garlic powder, salt, and pepper. Stir well and chill.
In a bowl, combine ground lamb, minced garlic, rosemary, mint, cumin, salt, and black pepper.
Gently form 3-4 patties, being careful not to overwork the meat. Lightly coat patties with olive oil or spray.
Season the outside of the patties with additional salt and pepper.
Preheat air fryer to 400°F (205°C) for 5 minutes.
Spray the air fryer basket with oil and place patties in a single layer.
Air fry for 8-10 minutes, or until internal temperature reaches 160°F (71°C).
Serve burgers on buns with tzatziki and your favorite toppings.