Chicken Shawarma with Yogurt Sauce

Name: Chicken Shawarma with Yogurt Sauce
Ingredients: ¾ cup whole-milk plain yogurt, divided; 1 small yellow onion, grated; 2 tablespoons lemon juice, divided; 3 cloves garlic, pressed or finely grated, divided; 2 teaspoons ground coriander; 2 teaspoons ground cumin; 1 teaspoon ground allspice; 1 teaspoon ground pepper; 1 teaspoon kosher salt, divided; ½ teaspoon ground turmeric; 2 pounds boneless, skinless chicken thighs; ½ cup finely chopped seeded cucumber; 2 tablespoons chopped fresh mint, cilantro and/or parsley; 3 whole-wheat lavash, halved; Lettuce leaves & sliced tomato for serving