Whisk together mayo, 3 minced garlic cloves, 1 tablespoon lemon juice, and pinch of salt for the sauce. Cover and refrigerate for at least 20 minutes.
Mix olive oil, cumin, paprika, turmeric, coriander, cinnamon, 4 minced garlic cloves, 2 tablespoons lemon juice, salt, and pepper in a large bowl.
Add sliced chicken to the spice mixture and toss until evenly coated. Marinate for 30 minutes at room temperature or up to 4 hours refrigerated.
Heat a large skillet over medium-high heat. Cook chicken in batches without crowding, 3-4 minutes per side until internal temperature reaches 165°F.
Transfer cooked chicken to a cutting board and rest for 5 minutes before slicing into strips.
Serve in warm pita bread with garlic sauce, diced tomatoes, cucumbers, red onion, and fresh parsley.