Combine lemon juice, oil, garlic, oregano, salt and pepper in an 8-inch glass baking dish. Add chicken and toss to coat. Marinate in the refrigerator, stirring once, for at least 20 minutes and up to 2 hours.
Position rack in upper third of oven; preheat broiler to high.
Transfer the chicken to a rimmed baking sheet. Broil on the upper rack until no longer pink in the middle, 5 to 7 minutes.
Meanwhile, combine lettuce, tomato and onion in a medium bowl.
To serve, spread 1 tablespoon tzatziki on each warmed pita and top with the chicken and the salad.
