1Place coriander, cumin, allspice, cinnamon, lemon juice, oil, tomato, onion and garlic in a food processor or blender; pulse to form a thick paste. In a bowl, combine lamb cubes, tossing to coat evenly. Cover and refrigerate for 2 hours.
2Skewer lamb and grill over medium-hot coals, turning every 2 minutes until well browned, but still juicy and slightly pink inside, 8 - 10 minutes. Place pita halves directly on the grill until just warmed, about 10 seconds per side.
3Using a fork, slide the lamb pieces from 1 skewer on to the pita. Top with a quarter of the lettuce, tomatoes, and mint. Spoon over lemon tahini sauce. Sprinkle with salt and pepper and roll up. Repeat with remaining pita, lamb, lettuce, tomatoes, mint and tahini sauce.
4For the sauce, whisk tahini, garlic and lemon juice together until smooth. Whisk in water. Add salt and pepper to taste. Cover and let stand at room temperature for 30 minutes to allow flavors to blend. Serve chilled or at room temperature. (Make sauce up to 2 days in advance - cover and refrigerate).