"Barzillai" is a scriptural name (other spellings are misspellings).

— born in Needham, Norfolk Co., MA:
  2.  Miriam LYON, b. 31 Jan 1768; d. 30 Jul 1820
  3.  Nathaniel LYON, b. 11 Feb 1770 — may be this Nathanial LYON, b. 1770, MA

— born Hubbardston, Worcester Co., MA:
  4.  Samuel LYON, b. 25 Nov 1771; d. young
  5.  Asa LYON, b. 4 Jan 1744
  6.  Martha LYON, b. 29 Feb 1776
  7.  Ruth LYON, b. 5 Apr 1778; d. 11 May 1858
  8.  Lucy LYON, b. 1780; d. 8 Feb 1826
  9.  Lois LYON, b. 1780
10.  [Elizabeth] Betsey LYON, b. 1782
11.  Anna LYON, b. 1784; d. 25 Deb 1851

1.  Marriage Record:

.  A[lbert] B[rown] Lyon(s) & G.W.A. Lyon, eds.  1905. Lyon Memorial: Massachusetts Families.  [Vol. I.]  Press of Wm. Graham Printing Co., Detroit, MI (page images online at Ancestry.com; transcription by DGM from hard copy original; color added by DGM):

p. 339

BARZILLAI5 LYON [Nathaniel,4 Nathaniel,3 Nathaniel,2 Peter1] was born in Roxbury, Mass., in Sept., 1739, and died in Hubbardston, Mass., June 24, 1796, ae. 57 y., killed by a falling limb while cutting timber.  He married in Needham, Sept. 25, 1765, Mary Davenport, who was born in 1742, and died April 1, 1803.  Barzillai, according to the History of Hubbardston, which styles him Bezaleel, came thither with his wife, Mary Davenport, from Barre, in 1771, and died in Hubbardston, 1796, at the age of 57.  This corresponds with the Roxbury

p. 340

birth record.  He was in Needham in 1770, as his son Nathaniel is recorded there [see also H.G.R. 32, 55, 56], though the son must have died early, as he is not mentioned by Stowe. Children of Barzillai and Mary (Davenport) Lyon, given by Stowe, were:   114.   I.   Sarah, b. 1767; m. 1st, Feb. 5, 1787, Paul Matthews (Princeton); he d. July 20, 17(?); she m. 2d, Luke Warren (or Warner); d. Jan. 30, 1804.   115.   II.   Miriam, b. Jan. 31, 1768 (Needham); m. June 26, 1804 (Hist. Hubbardston), Nathan Newton; 6 ch.; d. July 30, 1820.   116.   III.   Nathaniel, b. Feb. 11, 1770 (Needham); d. early (?).   117.   IV.   Samuel, b. Nov. 25, 1771; d. young.   *118.   V.   Asa, b. Jan. 4, 1774; m. Dec. 5, 1799, Attarah Grimes; d. Malden, _.   119.   VI.   Martha, b. Feb. 29, 1776; m. Joel Wheeler.   120.   VII.   Ruth, b. Aril 5, 1778; not m.; d. May 11 1858.   121.   VIII.   Lucy, b. 1780; m. Aug. 16, 1801, Jotham Stone; d. Feb. 8, 1826.   122.   IX.   Lois, b. 1780; m. Aaron Wright.   123.   X.   Betsey, b. 1782; m. 1st John Woodward; m. 2d Calvin Hinds.   124.   XI.   Anna, b. 1784; m. J. Pollock; d. Dec. 25, 1851. ...

I can't find in the book what "H.G.R." means.  Anyone know?

.  Stowe, J.M. [John Murdock].  1881.  History of the Town of Hubbardston.  "Published by the Committee," Hubbardston, MA (online at archive.org).  Nothing we don't already know, so I'll transcribe this later.  Like most authors of this era, he doesn't cite his sources, so we don't know why Stowe is calling him, "Bezeelel," but this is a different scriptural name from "Barzillai," so I suspect Stowe has erred.