Be careful not to confuse him with Thomas Henry Ham born Sep 1826, son of John Jackson Ham, who married Lucy’s sister Emily Thacker and moved to Missouri.

1850 census of Carter Co., Ky, district 2, enumerated 13 Sep, lists on p. 52 as family #324:
Robert Wood, 71, b. Va, farmer; Elizabeth, 52, b. Ky; Durret, 22, b. Ky; Thomas W. Ham, 20, b. Ky

The preceding household is the family of Joseph Ham age 58 with wife Nancy age 57.

In the 1850 census where she was listed with her parents, her birthplace is given as Virginia, but the 1860 and 1870 censuses both say Kentucky. The 1880 says Virginia.

1860 census of Rowan Co., Ky, enumerated 17 July, lists on p. 21 as family #154/158:
Thos Ham, 20; Lucy A., 21; Elizabeth, 6; America C. A., 4; Leeander L, 8/12. All born in Kentucky.

1870 census of Rowan Co., Ky, Pine Grove precinct, enumerated 25 June, lists on p. 12 as family #76:
Ham, Thomas, 38, farmer; Elizabeth, 16; America, 13; Leander, 11; Philip, 9; Leonard, 3; Lena, 1. All born in Kentucky.

1880 census of Rowan Co., Ky, Pine Grove precinct, enumerated 1 June, lists on p. 32 as family #234/254:
Ham, Thomas W., 51, blacksmith, b. Ky Va Ky; Lucy A., wife, 43, Va Va Va; Leander, 20, son; Phillip D., 18, son; Lenard M., 12, son; Lina S., 10, dau; William, 8, son. All children born Ky Ky Va.