Make the marinade: In a bowl, mix yogurt, olive oil, tomato paste, spices, lemon juice, salt, and pepper.
Add the meat: Toss the thinly sliced meat in the marinade. Mix well. Cover and refrigerate for at least 3 hours.
Cook the meat: Grill, pan-fry, or roast in the oven at 220°C (430°F) for 20–25 minutes until browned and slightly crispy.
Warm the bread: Heat the pita or flatbread in a dry pan or oven for a few seconds.
Assemble: Place the cooked meat in the center of the bread. Add lettuce, tomato, onion, and sauce.
Wrap and serve hot.