In a medium saucepan, stir chicken and Greek dressing together. Heat until warmed through.
Grate cucumber, squeezing out all excess moisture with your hands. In a small bowl, combine grated cucumber and remaining tzatziki sauce ingredients.
Warm pita bread in microwave about 20 seconds. Add desired amount of shredded lettuce, tomato, onion and chicken on top of each pita. Drizzle each gyro with a generous amount of tzatziki sauce and feta cheese. Fold gyro in half to serve.