The LDS Ancestral File calls her, "Hettie Catharine," but are they just mis-reading "Kittie"?  Or am I mistaken in thinking "Hetty" is a mis-reading of "Kitty"?  Hettie is the nickname for Hester, and that's not a typically German name — and these were Germans.

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

Lamb, William	Cuf, Hetty	15 Jun 1815	Fairfield Co.
Lamb, Sarah	Huber, Martin	29 Oct 1835	Fairfield Co.
Lamb, Elizabeth	Hite, Joseph	17 Oct 1836	Fairfield Co.
Lamb, Mary	Ruffner, Benjamin	2 Feb 1837	Fairfield Co.

Warning:  while the Elizabeth LAMB who married Joseph HITE is known to be the daughter of our subjects, my connecting this Sarah LAMB and this Mary LAMB to our subjects is entirely circumstantial and may be incorrect.

1b.  Jordan R. Dodd, ed.  1998.  Marriage Index: Ohio, 1851-1900.  Liahona Research, Orem, UT (Broderbund CD-236):

Lamb, Sophia

Tschopp, Henry

23 Dec 1852

Fairfield Co.

Same warning.

1c.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org):

REBECCA LAMB Spouse: HENRY ARNOLD Marriage: 16 Mar 1843, Lancaster, Fairfield, Ohio Source: patron submission

1d.  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):

CUF, HETTY-WM. LAMB-JUN 1815

2.  1820 Census Index and Digital Images (online at Ancestry.com; Image #3 of 4 — indexed as "Willam"; extracted by Diana Gale Matthiesen):¤•

1820

OH

Fairfield Co.

Walnut Twp.

p. 104

Ln. 12

Wm Lamb

100010-20010-0-100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= D.C.
1 male	26-44	1775-1794	= William (b. 1794)
2 females	9 or under	1810-1820	= Elizabeth = Sarah
1 female	26-44	1775-1794	= Catharine (b. 1794)
1	person engaged in agriculture

Listed between William's brothers, George LAMB and Peter LAMB, and three lines from Catharine's father, Valentine CUPP. 

3.  1830 Census Index and Digital Images (online at Ancestry.com; Image #33 of 34; extracted by Diana Gale Matthiesen):¤•

1830

OH

Fairfield Co.

Walnut Twp.

p. 200

Ln. 2

William Lamb

001 011 - 222 001

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-14	1815-1820	= D.C.
1 male	20-29	1800-1810	= ?
1 male	30-39	1790-1800	= William (b. 1794)
2 females	4 or under	1825-1830	= Mariah (b. 1830) = Catharine
2 females	5-9	1820-1825	= Rebecca (b. 1823/4) = Mary
2 females	10-14	1815-1820	= Elizabeth = Sarah
1 female	30-39	1790-1800	= Catharine (b. 1794)

Listed next to William's brother, Peter LAMB, who is next to Catharine's father, Valentine CUPP. 

4.  1840 Census Index and Digital Images (online at Ancestry.com; Image #12-13 of 24 — indexed as "Willaim", the numerical data pages preceded the name pages; extracted by Diana Gale Matthiesen):¤•

1840

OH

Fairfield Co.

Walnut Twp.

pp. 348A-348B

Ln. 21

Lamb William

010 010 100 - 112 200 100

0100000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	5-9	1830-1835	= William (b. 1834)
1 male	20-29	1810-1820	= D.C.
1 male	40-49	1790-1800	= William (b. 1794)
1 female	4 or under	1835-1840	= Minerva (b. 1836/7)
1 female	5-9	1830-1835	= Sophia (b. 1832/3)
2 females	10-14	1825-1830	= Mariah (b. 1830) = Catharine
2 females	15-19	1820-1825	= Rebecca (b. 1823/4) = Mary
1 female	40-49	1790-1800	= Catharine (b. 1794)
1	person engaged in agriculture

List was roughly alphabetized, so no neighborhood reconstruction is possible.

5.  1850 Census Index/Images (online at Ancestry.com; Image #48 of 51):  Walnut Twp., Dist. 41, Fairfield Co., OH, p. 219B, 1332/1332, enumerated 6 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Lamb William	55	M		Farmer	4800	Va
"  Catharine	55	F				"
Arnold Rebecca	26	F				O
"   Mary C	6	F				"
"   Jane	4	F				"
"   William	3	M				"
Lamb Mariah	19	F				"
"  Sophia	17	F				"
"  William	15	M		Farmer		"
"  Minerva	13	F				"

Listed next to William's brother, Peter LAMB (wife Mary WALTERS), who is next to Catharine's brother, Samuel CUPP (wife Magdalena WALTERS), who is next to Catharine's father, Valentine CUPP. 

6.  1860 Census Images (online at Ancestry.com; Image #4 of 54):  Pleasantville P.O., Walnut Twp., Fairfield Co., OH, p. 226B, PN 186, 1359/1359, enumerated 3 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Wm Lamb	65	M		Farmer	9000	100	Va
Catharine "	65	F					Do
Wm W      "	24	M		Farmer		900	Ohio
Maria     "	27	F		Domestic			Do
Minerva   "	22	F		???? School			Do
Rachel J Arnold	16	F				170	Do
Wm L       "	12	M				170	Do
Wilson Black	20	M		Farm laborer			Do

Rachel Jane and William L. ARNOLD are our subjects' grandchildren.  It appears their mother, Rebecca (CUPP) ARNOLD, has died, leaving them each a small bequest.  Has granddaughter Mary C. ARNOLD married or is she deceased?  They are listed next to William's brother, Peter LAMB, with whom is living John CULP (æ 11, b. OH), who is living two households from Catharine's brother, Samuel CUPP. 

7.  1870 Census Images (online at Genealogy.com; Image #1-2 of 60):  Lancaster P.O., Pleasant Twp., Fairfield Co., OH, pp. 275A-275B, PN 1-2, 8/8, enumerated 2 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Lamb William	76	M	W	Infirm	8000	200	Virginia
____ Catharine	76	F	W	Infirm			Virginia
[next page]
Reichort John	31	M	W	Farmer	800	800	Ohio
________ Minerva	33	F	W	Keeps house			Ohio
________ Elmer	2	M	W	At home			Ohio
________ Carin?	1	F	W	At home			Ohio
Culp George	32	M	W	Farmer		300	Ohio

8.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).

9.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org).