I had in mind more gentlemanly language, 'tis all.You might consider that your message and argument suffers as a result of your choice of "colorful" words and phrases.
Be that as it may, let's get back to genealogy. In particular the statement that the name Lawson cannot have metamorphosed from other forms of the name. It is really hard to understand why you insist upon that since it is well established that this is precisely what happened(outside of your overall attempt to make it appear that Doug has done something wrong--which he has not). Doug has pointed you to a learned and well-documented article on this very family that was published not so very long ago in the New York Genealogical & Biographical Record.
This positively, absolutely did happen. The name became Anglicized. Further, the Dutch name Annetje, also seen as Hannetje, became Anglicized to Anna and Hannah with constancy.