WARNING:  There is not a shred of evidence identifying Henry's parents, only secondary sources.
Father possibly:  Richard LYON
or
Father very doubtfully:  John LYON
Mother very doubtfully:  Eupham GLEDSTANES
or 
Father definitely not:  Sir Glenn LYON
Mother definitely not:  Lady Priscilla BOWES

— by deduction, born in Newark, East Jersey Province:
7.  Benjamin LYON, b. ca. 1668; m. Bethia CONDIT — 6th great-grandparents of Barbara PIERCE, wife of President George H.W. BUSH
8.  Ebenezer LYON, b. 1669/70 

1.  Family Group Sheet compiled by Betty Ann (Matthiesen) Cogliati.

2.  Clarence Almon Torrey.  1997.  New England Marriages Prior to 1700.  Genealogical Publ. Co., Baltimore, MD.  On p. 481:

LYON, Henry (-1703) & 1/wf ?Elizabeth/?Mary BATEMAN; b 1653; Milford, CT / Elizabeth, NJ / Newark, NJ

The "b 1653" refers to the birthyear of the earlist known child, as an approximate indicator of marriage year.  Locations are known residences of the husband, ending with his place of death.

3.  The Old Newark Burying Ground, which cites "Essex County Gravestones" by E.A. Baldwin (Genealogical Magazine of New Jersey).

LYON, Mr. Henery - died 23 Mar 1707 aged 84 yrs

This would make Henry born in 1622 or 1623, depending on whether he'd had his birthday yet that year, though most likely in 1623 as the New Year was only two days away and he'd probably had his birthday.  Or, if this year is the "old system," which presumably it was, then by our calendar he died in 1708 and was born in 1623 or 1624, more likely 1624. 

4.  James Savage.  1860-62.  A Genealogical Dictionary of the First Settlers of New England.  Little, Brown & Co., Boston (reprinted 1965, Genealogical Pub. Co., Baltimore; online at GenealogyLibrary.com).  Section on William Bateman on pp. 90-91, in which William mentions son-in-law, Henry Lyon, in his will. 

5.  Colonial America, 1607-1789 NJ Census Index (online at GenealogyLibrary.com):

1670	Lyon, Henry	NJ	Essex Co.	Newark		p. 239
1685	Lyon, Henry	NJ	Essex Co.	Elizabethtown		p. 238
1696	Lyon, Henry	NJ	Essex Co.		Quit Rent	p. 375
1696	Lyon, Henry	NJ	Essex Co.		Quit Rent	p. 378

In 1685, Henry Lyon is on the Quit Rent rolls of Newark, not Elizabethtown. 

6.  David Lawrence Pierson.  1917.  Narratives of Newark (in New Jersey) from the Days of Its Founding.  Pierson Publ. Co., Newark, NJ (online at GenealogyLibrary.com). Extract of mention of LYON.  On pp. 10-11 is the "Fundamental Agreement" forming the "constitution" of Newark.  Henry LYON signed the agreement on 24 June 1667 (he was not one of the original signers on 30 Oct 1666).  He signed with his name, not a mark, so he was able to write. 

7.  Royal R. Hinman.  1852.  A Catalogue of the Names of the Early Puritan Settlers of the Colony of Connecticut.  Press of Case, Tiffany, & Co., Hartford (online at GenealogyLibrary.com).  Another version of the "constitution" of Newark, this time called the " Plantation Covenant," but this time including the towns of origin of the signers. 

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

CHARLES ANDERSON BOSTON, of New York City, b. 30 Aug. 1863; m. Ethel Gustava, dau. of Edward Lyon, of New York City, a descendant of Richard Lyon, of Perthshire, Member of Cromwell's Army, who emigrated to America in 1648, son of John Lyon, of Auldbar, and grandson of Sir Thomas Lyon, styled Master of Glamis (d. 1608) and his wife, Eupheme, dau. of the 7th Earl of Morton.  Sir Thomas Lyon was the son of John Lyon, 7th Lord Glamis (see BURKE'S Peerage, STRATHMORE, E.).

On the assumption that Richard is Henry's brother, then this is Henry's ancestry, too.

9.  Sidney Elizabeth Lyon, Louise Lyon Johnson, and A.B. Lyons, eds.  1907.  Lyon Memorial:  Families of Connecticut and New Jersey, including Records of the Descendants of the Immigrant Richard Lyon of Fairfield, Henry Lyon of Fairfield, with a Sketch "Lyons Farms" by S.R. Winans, Jr.  Press of William Graham Printing Co., Detroit, MI.

10.  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 (Ted and Elenor Lyons, 524 Mark Lane, Belton, MO 64012-1829-10).

11.  Brief mention in the June 2000 issue of The Lyon's Tale (published by the Lyon(s) Family Assn.) that the parents of Henry, Thomas, and Richard were Sir Glenn LYON (1570-1643) and Lady Priscilla BOWES (1573-1638).  Documentation has been requested from the Association.
UPDATE:  the submitter of the 'Glenn LYON - Priscilla BOWES' pedigree paid to have this research done in England. I have seen the report, which is totally undocumented, and I have no doubt whatsoever that the pedigree is bogus and that the purchaser was scammed.  Let's hope a very strong retraction is printed because otherwise this thing will never die.  I should emphasize that I do not blame the submitter for this fiasco — the submitter is guilty only of trusting what sounded, to an apparently novice genealogist, like a legitimate, professional source.  It's a little harder to understand how this item slipped by the editors...  It's too bad this had to happen.  No winners here, except the scumbag who pocketed the money.  [For further discussion and text of the pedigree, please see this page.] 

12.  Frederick A. Virkus.  1927.  The Abridged Compendium of American Genealogy.  Vol. I.  F.A. Virkus, Chicago.  On p. 593 (boldface added):

Henry Lyon (ca. 1625-1703), from Scotland to New Milford, Conn., 1648, one of the first settlers at Newark, N.J., 1666, where was dep. mem. Council and first treas., removed to Elizabeth Town, N.J., but returned to Newark, m 1652, Elizabeth Bateman...

13.  Richard W. Cook.  1996.  "The Thomas Osborn Family."  Pages 627-681 in Genealogies of New Jersey Families.  Vol. I.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-182).  On p. 634 (boldface added):

Then on Aug. 19, 1690, Henry Lyon deeded Thomas Osborne, both of Elizabeth Town, 20 acres adjoining the grantor (NJA 21:185).

NJA = New Jersey Archives.

14.  Charles Carroll Gardner.  1996.  "A Genealogical Dictionary of New Jersey:  Abbott (Abbett, Abbitt, Abit)."  Pages 17-26 in Genealogies of New Jersey Families.  Vol. II.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-182).  [Boldface added.]

p. 22

Dec. 28, 1682, John Cat-

p. 23

lin and Daniel Abbot (signs Abet), both of Newark, made an agreement whereby Daniel was to buy "one certaine out plantacon, Dwelling house Edifices and othe buildings" in the bounds of Newark, at the mountain, for the sum of £40., payable in instalments over a period of three years, the property to revert to the seller in the event of any default in payment.  On Feb. 20, 1682/3 John Catlin, by an endorsement on the back of the deed, quit-claimed to Henry Lyon all of his interest in the contract, including the right of re-entry in the event of nonpayment.  (EJD A:19).

EJD = East Jersey Deeds, Secretary of State's Office, Trenton, NJ.

15.  David Dobson.  1985.  Directory of Scottish Settlers in North America, 1625-1825.  Vol. 5.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-354).  On p. 145 (boldface added):

Primary Individual: Lyon, Henry; Place: America; Year: 1649. Date of emigration and intended destination or place and date of first mention of residence in the New World.

16.  Frederick A. Virkus, ed.  1964/86.  Immigrant Ancestors: a List of 2500 Immigrants to America before 1750.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-354).  On p. 46:

Primary Individual: Lyon, Henry; Place: Connecticut; Year: 1648.

17.  Donald Whyte.  1972/81.  A Dictionary of Scottish Emigrants to the USA. Vol. 1.  2nd pr.  Magna Carta Book Co., Baltimore, MD (Broderbund CD-354).  On p. 208:

Primary Individual: Lyon, Henry; Place: Connecticut; Year: 1648. Compiled from correspondence and monument inscriptions...  Prepared for the Scottish Genealogical Society.

18.  Meredith B. Colket, Jr.  1975.  Founders of Early American Families: Emigrants from Europe, 1607-1657.  General Court of the Order of Founders and Patriots of America, Cleveland, OH (Broderbund CD-354).  On p. 185:

Primary Individual: Lyon, Henry; Place: Connecticut; Year: 1649.

19.  William Richard Cutter.  1913.  New England Families:  Genealogical and Memorial.  Vol. IV. Lewis Historical Publ. Co., New York, NY (reprinted for Clearfield Co. by Genealogical Publ. Co., Baltimore; online at GenealogyLibrary.com).  There is a segment on LYON on pp. 2073-4. 

20.  New Jersey Archives, 1664-1703.  Vol. 21, p. 184.  Extract found in the Archives of the NJEssex-L mailing list (online at RootsWeb.com).  On p. 185 (boldface added):

1690-1 Mar 24.  Do. Isaac Whitehead of Elizabeth Town, cordwainer, and wife abigail, to Samuel Whitehead of Southampton, L.I., cordwainer, for 45 acres in the bounds of Elizabeth Town, S.E. Joseph Meeker, S.W. Henry Lyon, N.W. unserveyed land, N.E. a road; also 8 acres of meadow there, S Mr. Woodruff, N. and E. unserveyed meadows, W. a small creek.

21.  Donald Lines Jacobus.  1930-32.  History and Genealogy of the Families of Old Fairfield.  Fairfield, CT (reprinted 1976/91 by Genealogical Publ. Co., Baltimore; Broderbund CD-515).  On p. 393:

Lyon, Henry.   Admitted to Milford Church, 25 Feb. 1648/9; dismissed to Fairfield; where he was granted a homelot, 1652.  He m. a dau. of William Bateman.   He entered for record at Fairfield, 9 Feb. 1655 [1655/6], land purchased of Richard Lyon, a house purchased of William Bateman, and land given him by the latter.   He rem. to Newark, N.J.

22.  Susan Woodruff Abbott, compiler; Jacquelyn L. Ricker, ed.  1979.  Families of Early Milford, Connecticut.  Genealogy Publ. Co., Baltimore, MD (Broderbund CD-515).  On p. 410:

LYON 1.  Henry Lyon was not a freeplanter in 1639 but had 3 acres of land alloted (sic) to him, Lot #26.  He was admitted to the church in Milford 25 Feb 1648, but was dismissed to Fairfield church.  He married a daughter of William Bateman and removed to Newark, N.J.

23.  Frank R. Holmes.  1923.  Directory of the Ancestral Heads of New England Families, 1620-1700. American Historical Society, New York (republished 1964-99 by Genealogy Publ. Co., Baltimore; Broderbund CD-504).  On p. 154:

LYON... HENRY, came from Glen Lyon, Perthshire, Scotland, to Milford, Mass., 1648, removed Fairfield, Conn., 1652.

24.  Henry Whittemore.  1898-1906.  Genealogical Guide to the Early Settlers of America.  Excerpted and reprinted from The Spirit of '76, vols. V-XII (reprinted 1967 by Genealogical Publ. Co., Baltimore, MD; Broderbund CD-504).  On p. 341:

LYON, HENRY, Milford, 1646, was of Fairfield, 1652, where he married the only daughter of William Bateman.

25.  Royal R. Hinman.  1852.  A Catalogue of the Names of the Early Puritan Settlers of the Colony of Connecticut...  Press of Case, Tiffany, & Co., Hartford (online at GenealogyLibrary.com).  On p. 116, in a sketch of Rev. Ebenezer BALDWIN:

...The Record of Newark, and Conger, both say that Catlin and his wife, Mary, were at Newark until about 1682, when Catlin sold out to Henry Lyon...

26.  Messages in the Lyon Family Genealogy Forum (online at GenForum.com).

27.  Encyclopedia Britannica CD-98.