Combine oregano, garlic powder, 1/2 teaspoon pepper, and 1/4 teaspoon salt in a bowl. Heat a nonstick skillet over medium-high heat. Coat pan with cooking spray. Add chicken and spice mixture; sauté until chicken is done. Drizzle with 1 tablespoon juice; stir. Remove from pan.
Combine remaining 2 teaspoons juice, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, yogurt, tahini, and garlic in a small bowl; stir well. Combine lettuce, cucumber, tomatoes, and olives. Place 2 1/2 cups of lettuce mixture on each of 4 plates. Top each serving with 1/2 cup chicken mixture and 1 tablespoon cheese. Drizzle each serving with 3 tablespoons yogurt mixture.