Lessa specified that it must be kept secret, because no one in her day and age knew what had happened to the other five Weyrs. She told the Masterharper he had to write the Question Song, because it had given her important clues, but wouldn't tell him exactly what the words had to be.
It was only her mistake when learning how to fly between that led her to realise dragons could even travel through time. Benden Weyr at the end of the Eighth Interval was short of dragons and a lot of the old records were unreadable, too.