Jacob was nearly 20 years older than Mary CULP, so we would expect him to have had earlier children, and the censuses show he had at least one.

1a.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

LAMB, Jacob

CULP, Magdalene

19 Aug 1806

Fairfield Co.

1b.  Fairfield County Marriages, 1800-1811 (online at the web site of the Fairfield County Chapter of the Ohio Genealogy Society):

LAMB, Jacob//CULP, Magdalina; license 18 Aug 1806; married 19 Aug 1806; Elnathan Scofield, JP; PAA-22

P = Probate Book-Page (e.g., PAA-8 = Probate Marriage Book A, Part A, Page 8)

1c.  Fairfield County, Ohio, Marriages extracted from "Ye Ancient Swains" Column in the Lancaster Gazette, 1801-1836 (online at the web site of the Fairfield County Chapter of the Ohio Genealogy Society):

CULP, MAGDALENA - JACOB LAMB - AUG 1806

2.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):  there was no Federal Census in Ohio in 1800 (it was not yet a state); tax lists are substituted on this CD, where available.•

1806 Tax List	Lamb, Jac	OH	Fairfield Co.	p. 27
1806 Tax List	Lamb, Jacob	OH	Fairfield Co.	p. 27
1806 Tax List	Lamb, Jacob	OH	Fairfield Co.	p. 53
1806 Tax List	Lamb, Jacob	OH	Fairfield Co.	p. 60
1807 Tax List	Lamb, Jacob	OH	Fairfield Co.	p. 14
1808 Tax List	Lamb, Jacob	OH	Fairfield Co.	p. 19

I have no explanation for the number of Jacob's in 1806.  It was down to one in 1810.

3.  Census Index:  U.S. Selected Counties, 1810 (Broderbund CD-313):  the 1810 Ohio census was lost (except for Washington Co.); tax lists are substituted on this CD, where available.•

1810 Tax List

Lamb, Jacob

OH

Fairfield Co.

p. 24

4.  1820 Census Index and Digital Images (online at Ancestry.com; Image #5 of 5 — mis-linked to Image #4 and mis-indexed as being in Clear Creek Twp.; extracted by Diana Gale Matthiesen):•

1820

OH

Fairfield Co.

Richland Twp.

p. 96A

Ln. 1

Jacob Lamb

220001-20110-0-100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1810-1820	= William (b. 1815) = Isaac (b. 1812)
2 males	10-15	1804-1810	= Peter (b. 1809) = Henry (b. 1807)
1 male	45 or over	in or bef. 1775	= Jacob (b. 1768)
2 females	9 or under	1810-1820	= Hannah (b. 1819) = Sarah (b. 1817)
1 female	16-25	1794-1804	= Daughter A
1 female	26-44	1775-1794	= Magdalene (b. 1787)
1	person engaged in agriculture

5.  1830 Census Index and Digital Images (online at Ancestry.com; Image #11 of 16; extracted by Diana Gale Matthiesen):•

1830

OH

Fairfield Co.

Richland Twp.

p. 258

Ln. 17

Jacob Lamb

020 220 001 - 112 010 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	5-9	1820-1825	= David (b. 1825) = Jacob (b. 1823)
2 males	15-19	1810-1815	= William (b. 1815) = Isaac (b. 1812)
2 males	20-29	1800-1810	= Peter (b. 1809) = Henry (b. 1807)
1 male	60-69	1760-1770	= Jacob (b. 1768)
1 female	4 or under	1825-1830	= Rebecca (b. 1827)
1 female	5-9	1820-1825	= Mary (b. 1821)
2 females	10-14	1815-1820	= Hannah (b. 1819) = Sarah (b. 1817)
1 female	20-29	1800-1810	= Daughter A
1 female	40-49	1780-1790	= Magdalene (b. 1787)

6.  1840 Census Index/Images (online at Ancestry.com; Image #9 of 20; extracted by Diana Gale Matthiesen):•

1840

OH

Fairfield Co.

Richland Twp.

p. 380B

Ln. 10

Lamb Marey

000 200 - 000 100 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	15-19	1820-1825	= David (b. 1825) = Jacob (b. 1823)
1 female	15-19	1820-1825	= Mary (b. 1821)
1 female	50-59	1780-1790	= Mary (b. 1787)
1	person employed in agriculture

List was roughly alphabetized.

7.  1850 Census Index/Images (online at Ancestry.com; Image #1 of 41):  Richland Twp., Fairfield Co., OH, p. 386A/769, 4/4, enumerated 14 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):•

Jacob Lamb	27	M		Farmer		O
Mary    "	62	F			6750	Va
Mary    "	29	F				O
Joseph Edwards	16	M		Laborer		O
Issaac Lamb	38	M		Farmer		O
David    "	8	M				O
M L      "	6	F				O

It appears Isaac has returned home a widower with two children.  Living next door to Mary's son, William LAMB (æ 36, b. OH, wife Mary A.).