Whisk oil, lemon juice, garlic, and spices in a bowl; toss with chicken.
Marinate chicken for 10–30 minutes.
Sear chicken in a skillet over medium-high heat for 5–6 minutes until cooked through.
Briefly warm pitas in a skillet or microwave until soft.
Spread tzatziki inside or on top of the warm pita.
Layer with lettuce, cooked chicken, and the tomato-cucumber-onion mixture.
Sprinkle with feta cheese and optional parsley.
Fold or stuff and serve immediately.