Interesting to see that DNA data set that suggests a close relationship between two of the several different Lyon men who immigrated to early colonial New England.
Researchers should nail down the lineage of each of these tested men before drawing firm conclusions. The genealogy of the Lyons in New England can be confusing. I have spent a lot of time puzzling over records for different men named Seth Lyon who were born at roughly the same time and lived in close proximity at the time of the first several U.S. censuses, and I believe I read recently that Chris Child of NEHGS had discovered a Lyon from the Fairfield line who had settled in Woodstock, Connecticut, alongside various Lyons from the Roxbury line. The chance of attaching a Lyon to the wrong lineage seems high, so careful work is needed to confirm the lineages of the Lyon men who have tested.
As for the British ancestry, a while back I found that at least one of the claimed British lineages for people named Lyon is probably downright fraudulent. I see that one of the tested individuals on that website claims descent from William LYON (1620-1692) Heston, Middlesex > MA, i.e., the same person as "William Lyon of Roxbury" (who I believe is my Lyon immigrant ancestor). William's alleged origin in Heston, Middlesex, derives from the work of fraudulent genealogist Albert Welles (see Category: Albert Welles Fraud). The English baptism record that has been identified as possibly being the baptism of this William Lyon does not seem to exist, it may be a fabrication by Welles.
So it seems to me that the best chance of finding common ancestry for Richard of Fairfield and William of Roxbury lies in Britain -- from DNA testing of men with Lyon ancestry whose families haven't moved around much over the centuries.