In a large bowl, whisk together the olive oil, lemon juice, minced garlic, ground cumin, ground coriander, paprika, turmeric, cayenne pepper, salt, and black pepper.
Add the chicken thighs and toss until well coated. Cover and refrigerate for at least 1 hour to allow the flavors to meld.
Heat a grill pan (or outdoor grill) over medium-high heat. Place the marinated chicken on the grill and cook for about 6-8 minutes on each side, or until the chicken is nicely charred and cooked through. Remove the chicken from the heat and let it rest for 5 minutes before slicing thinly.
In a small bowl, mix the Greek yogurt, minced garlic, lemon juice, salt, and pepper to create a simple sauce.
Open the pita pockets or spread out the flatbreads, then layer with lettuce, tomato slices, red onion slices, and the sliced chicken. Drizzle the yogurt sauce over the top and serve immediately.