Squeeze horned melon into a fine mesh strainer over a bowl; press seeds with the back of a spoon to extract juice. Discard seeds. Add fresh lemon juice, 1/4 teaspoon salt, ground cumin, and yogurt to bowl; stir with a whisk. Cover and chill.
Place chicken breast halves between 2 sheets of heavy-duty plastic wrap; pound each piece to 1/2-inch thickness using a meat mallet or small heavy skillet. Sprinkle both sides of chicken with remaining 1/4 teaspoon salt and pepper; rub with garlic.
Heat 1/2 teaspoon olive oil in a nonstick grill pan coated with cooking spray over medium-high heat. Add 2 breast halves to pan; cook 4 minutes on each side or until done. Remove from heat, and keep warm. Repeat procedure with remaining 1/2 teaspoon oil and chicken. Transfer chicken to cutting board, and cool slightly. Cut chicken into thin strips. Fill each pita half with about 1/2 cup chicken, and top with 2 tablespoons raita.