1.  Marriage Record:

2.  Sidney Elizabeth Lyon.  1907.  Lyon Memorial:  Families of Connecticut and New Jersey.  Self-published, Jeffersonville, IN (facsimily reprint available from Higginson Books; online at Ancestry.com).

RHODE ISLAND LYONS. PROBABLY OF THE FAMILY OF HENRY.
p. 249	In the "Lyon Memorial, Maassachusetts Families" there is given a record of the descendants of a certin John Lyon of Scituate, R.I., born probably about 1740, whose parentage had not been ascertained, but who was referred doubtfully to the family of William1 Lyon of Roxbury.  It was stated, however, that he might have been a descendant of Henry1 Lyon.  No new light has been shed upon the question of his ancestry, but additional facts have been ascertained about other Rhode Island Lyons who seem to have been of the same family, and these may be given place here as being perhaps not out of their natural connection.  We have seen that one branch of the family of Henry established itself in Rhode Island, descendants of Lieutenant James Lyon (No. 26).  James had a brother John who married but whose descendants have not been traced.  It is quite possible that he also settled in Rhode Island, and it would have been very natural for him to name one of his sons John.  Another son he might naturally have named for his uncle Thomas.
Emphasis in red mine.  First of all, you are going to have to convince me that Lt. James LYON of Newark, NJ, is the same James LYON who lived in Newport, RI.  The author supplies no evidence supporting that he was.  And if they aren't the same man, that means none of Henry's descendants, in the early generations, moved to Rhode Island — a move that makes very little sense to begin with.  All the given names here (viz., John, James, and Thomas) are far too common to be used to support connections — who didn't name a son John?!

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

p. 13	20. John LYON (4.Samuel2, 1.Henry1) b. 1678, Newark, Essex Co., NJ, m. Elizabeth RIGGS, b. 1679. John's descendants have not been traced definately, but it is possible that he had sons, Joseph, John, and Thomas. Children: + 59. i  Thomas LYON b. late 1730s.
Emphasis in red mine.  One does wish they hadn't speculated here.  Bad connections, once published, are difficult to eradicate.