Preparation Preheat oven to 425°F. Combine cumin, coriander, paprika, cayenne, cinnamon, 2 Tbsp. oil, 3/4 tsp. salt, and 1/4 tsp. pepper in a large bowl. Add chicken and toss to coat. Spread on a rimmed baking sheet and roast until an instant-read thermometer inserted into the thickest part of thigh registers 165°F, 12–15 minutes; wrap pitas in foil and warm in oven during the last 5 minutes of cooking. Meanwhile, mix yogurt, tahini, garlic, lemon zest, 2 Tbsp. lemon juice, 1/2 tsp. salt, and 1/4 tsp. pepper in a medium bowl until incorporated. Fold in 2 Tbsp. dill and 2 Tbsp. mint. Toss cucumber, lettuce, tomatoes, onion, remaining 2 Tbsp. lemon juice, 2 Tbsp. oil, 1/4 tsp. salt, and 1/4 tsp. pepper in another medium bowl. Thinly slice chicken. Place 1 warmed pita on each plate and top evenly with chicken and tomato-cucumber salad. Drizzle each pita with 2 Tbsp. tahini-yogurt sauce; top with dill and mint. Serve remaining tahini-yogurt sauce alongside. Do Ahead Tahini-yogurt sauce can be made 1 day ahead. Cover and chill.