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 preferably overnight for better flavor.
Preheat your grill or a 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 fully cooked and the internal temperature reaches 165°F. Remove from heat and let rest for 5 minutes.
While the chicken is resting, prepare the garlic sauce by combining mayonnaise, Greek yogurt, minced garlic, lemon juice, salt, and pepper in a small bowl. Mix until smooth.
Slice the chicken into strips. Serve in pita bread or flatbreads with fresh vegetables and drizzle with garlic sauce.