Combine beans and water in a small microwave-safe bowl; cover with plastic wrap. Microwave at high 1 1/2 minutes or until beans are crisp-tender; drain. Rinse with cold water. Drain well; cool. Combine beans, olives, capers, and tuna.
Combine oil, juice, and salt, stirring with a whisk. Pour oil mixture over tuna mixture; toss gently to coat.
Line each pita half with 1 lettuce leaf; spoon about 1/2 cup tuna mixture into each lettuce-lined pita half.