Robert apparently carried on with Lucy Steele in secret, since John Dashwood never says in his letters, "We thought he was only trying to convince Lucy to break the engagement," or anything of that sort.
But, I find that hard to swallow, considering Robert's vanity, and inability to talk about anyone except himself. Do you think he managed secrecy on this occasion? That, maybe, Robert CAN keep a secret, when he glories in imagining the final reveal that will surprise and please his family when his self-imposed mission is complete? ? Or that Robert did tell part of it, and John Dashwood did not think it necessary to explain what PART of Robert's actions were carried on in secrecy? Or do you think Lucy just worked THAT quickly -- that Robert had no time to tell the tale, because it was only a few visits that were needed to convince him that Lucy would make himself a good wife?