In a large bowl, combine olive oil, cumin, coriander, smoked paprika, turmeric, cinnamon, cayenne pepper, minced garlic, salt, black pepper, and lemon juice. Mix well to create a marinade.
Add the chicken thighs to the marinade, ensuring they are well coated. Cover and refrigerate for at least 1 hour, or preferably overnight for maximum flavor.
Preheat your grill or oven to 400°F. If using a grill, oil the grates to prevent sticking.
Remove the chicken from the marinade and discard any excess marinade. Grill the chicken for about 6-7 minutes per side, or until fully cooked and the internal temperature reaches 165°F. If baking, place the chicken on a baking sheet and bake for 25-30 minutes.
While the chicken is cooking, prepare the garlic sauce by combining Greek yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a bowl. Mix until smooth and creamy.
Once the chicken is cooked, let it rest for 5 minutes before slicing it into thin strips.
Serve the sliced chicken with the garlic sauce, along with pita bread, fresh vegetables, and your choice of toppings.