Our subject is said to have these parents, but there is zero evidence supporting the connection:
Father:  Nathaniel³ LYON
Mother:  Esther WHITE

1.  A.B. [Albert Brown] 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):

p. 333

NATHANIEL4 LYON (? Nathaniel,3 Nathaniel,2 Peter1] born about 1710, married in Roxbury, Mass., Sept. 17, 1734, Mary Lyon§ (Roxbury); died Sept. 22, 1760 (Needham). This is the Nathaniel who was assumed in loco to be of Peter's line.  All that is realy known of him is a few data from Needham records, and this extract from the Probate Records:  Mary Lyon, of Needham, widow, appointed Oct. 24, 1760, administratrix of the estate of her late husband, Nathaniel Lyon, by Amos Fuller, Josiah Newell and Aaron Smith, May 1, 1761.  Amout, £322—3s.—4½d.  Oct. 7, 1763, account of Mary, admx.  Allowance of sum of £10 paid to Barzillai Lyon; £6—13s.—4d. to Thomas Lyon, £14—6s.—8d. to Samuel Richards, etc.  Oct. 2, 1761, Caleb Kingsburg, Robert Fuller and Robert Smith appointed to divide estate of Nathaniel Lyon.  They reported Oct. 27 an appraisal, and that real estate would not admit of division.  Division: The two sons refused to accept the settlement of the estate upon them, and it was settled upon Elisha Mills, a son-in-law, and his wife Deborah, dau. of said Nathaniel; they to pay Barzillai, the eldest son of deceased, £43—3s.—6d., and to Elizabeth, Mary, Nehemiah and Hannah, the other children of said Nathaniel, £21—11s.—9d. on or before April 1, 1765; they also to pay Barzillai £25—10s—10d., and the other children named £11—5s.—5d. more within one year after the death of their mother, the widow Mary.  Dated Oct. 28, 1763. Children of Nathaniel and Mary (Lyon) Lyon, born in Roxbury (T.R.):     55.   I.   Joshua, b. March 30 (?), 1735; bapt. June 8, 1735; d. before 1761.   56.   II.   Deborah, b. Sept. 24, 1737; m. 1st May 10, 1759, Elisha Mills [Needham Epitaphs]; m. 2d about 1777, Aaron Smith (Dedham Hist. Reg.)   *57.   III.   Barsillai [Barzillai], b. Sept., 1739 [Ch. R. has "Aaron, son of Nathaniel and Abigail, bapt. Oct. 14, 1739"]; m. Sept. 25, 1765, Mary Davenport; d. June 24, 1796. §It seems probable that this Mary was of the family of William of Roxbury.  She was certainly a member of the Eliot Church in Roxbury.

p. 334

58.   IV.   Elizabeth, b. Feb. 6, 1742; bapt. ["Eliza"] Feb. 28, 1742 (Ch. R.); (?) m. Feb. 10, 1761, Zaccheus Bemis† (Lancaster).   59.   V.   Nathaniel, bapt. April 5, 1747 (Ch. R.); d. before 1761.   60.   VI.   Nehemiah, b. Feb. 21, 1750; bapt. March 4, 1750; m. int. March 5, 1774, Hepzibah Robinson (Princeton).   61.   VII.   Mary, b. March 20, 1753 (Needham T. R.); bapt. April 1, 1752(?); living in 1761.   62.   VIII.   Hannah, b. Sept. 19, 1755 (Needham T. R.); bapt. Aug. 21, 1755(?) (Roxbury Ch. R.); m. April 10, 1777 Daniel Wight (Ded.). ... †Probable since Elizabeth, who m. Zaccheus Bemis, was of Westminster, a town adjoining Hubbardston, where the brothers of Elizabeth above resided.

.  Lyon(s) Families Association of America: Database (on CD as of 22 Feb 2010; these are member submissions).