The reclusive author of “To Kill a Mockingbird,” one of the most acclaimed novels of the 20th century, says she never gave her approval to a new memoir that portrays itself as a rare, intimate look into the lives of the writer and her older sister in small-town Alabama. “Rest assured, as long as I am alive, any book purporting to be with my cooperation is a falsehood,” Harper Lee said in a letter released earlier this week, just as the new book, “The Mockingbird Next Door: Life with …