A.B. Lyon & G.W.A. Lyon, eds.  1905.  Lyon Memorial:  Massachusetts Families.  Wm. Graham Printing Co., Detroit, MI. 

The editor asserts this pedigree is "confirmed by research in England by the compilers"; however, as they include no documentation, their work must be considered unproven.  Whether their work was mere self-deception or deliberate, we'll never know, but I'm inclinced to believe the former.  Untrained researchers tend to have a low threshold for proof, and it's all too easy to accept something you want to believe.  We need to appreciate what a different cultural milieu they lived in.  In their day, the pressure to have illustrious ancestors was immense.

June Cioppettini, Lynda McGinnis, & Betty Cogliati, eds.  1999.  Henry Lyon of MA, CT, & NJ, and Some of His Lineage.  Lyon(s) Family Association of America, Belton, MO.

The connections here were innocently copied from Lyon & Lyon (1905) on the naive assumption that, having long been accepted, they must have been correct — and I know it was naive innocence because one of the editors was my aunt, Betty Ann (Matthiesen) Cogliati.  She had believed the above source all her life and would never, in a million years, have deliberately deceived anyone.  If someone had published a book on your ancestry, you simply assumed it must be true.  We need to appreciate how difficult it was to do genealogy before the advent of the internet and other aids to swift communication — her years of work on Lyon genealogy were done the hard way, via letters.  My one consolation in her passing is that she didn't live to see her beliefs in her allegedly royal Lyon ancestry overturned, and I feel guilty debunking it, even now. 

Directory of Royal Genealogical Data  by Brian C. Tompsett.

Sir John Bernard Burke.  1939.  Genealogical and Heraldic History of the Landed Gentry.  16th ed.  Burke's Peerage, London (American section reprinted 1996 as Burke's American Families with British Ancestry.  Genealogical Publ. Co., Baltimore, MD), p. 2572.

The connection of the New England LYONS — Thomas of Rye, Richard of Fairfield, and Henry of Newark — to the royal ones is fabricated mythology.  The connection never was proven and, based on what is known, was never even likely to have been true.

DNA testing has shown Richard and Henry are closely related to each other and to William of Roxbury, meaning their geographic origin is probably the same as William's, that is, in Middlesex, England, not Scotland.

Thomas is not related to them, and his one DNA connection is with an allegedly French LYON (more work needs to be done to prove his match really did originate in France).  In any case, he's not related to the other three.