In a large bowl, combine olive oil, cumin, coriander, 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 up to overnight for best flavor.
Preheat your grill or a large skillet over medium-high heat. Remove the chicken from the marinade and discard any excess marinade.
Grill or cook the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F and the chicken is nicely browned.
While the chicken is cooking, prepare the garlic sauce by whisking together yogurt, mayonnaise, apple cider vinegar, Dijon mustard, and salt in a small bowl. Adjust seasoning to taste.
Once cooked, remove the chicken from the heat and let it rest for 5 minutes before slicing it into thin strips.
Serve the sliced chicken in pita bread or flatbreads, topped with fresh vegetables and drizzled with garlic sauce.