Alas, Richard Atherton, Sheriff of Lancaster and founder of his family is a myth.
It is common in Heraldry for a man who has gained a proper achievements of arms to recite a pedegree based on what he may have been told but for which there is no evidence and it matters little to the herald . In one case a man claimed a right to certain healdry in a Court of Honour because he said that his family had used these particular symbols since the time of King Arthur and this was accepted with no evidence. I have the list of Lancastrian Sheriffs from 1087 to 1815 and there was no Atherton during the reighn of John or 100 years either side of the Reighn of King John.
Things that are repeated again and again can take on the mantle of truth if men wish to believe in these things or if it seems credible. Again. Here I am in Lancashire with the list of men who served as the Crowns Sheriffs. During "the High Middle Ages" men who served as Sheriffs were the trusted friends of the ruling King and not ordinary or common men.