Make the white sauce by blending mayo, sour cream or yogurt, garlic, sugar, lemon juice, and black pepper until smooth.
For the spicy rice, soak rice for 30 minutes, then rinse. Sauté garlic and tomato paste, add rice and spices, then simmer in chicken broth until cooked.
Marinate lamb with olive oil and spices, then cook in a skillet until browned.
Assemble bowls with rice, lettuce, tomatoes, lamb, and pita. Drizzle with white sauce, hot sauce, and optionally barbecue sauce.