He is refered to as Carey in the 1850 and 1860 censuses, as Cary on the birth record for his daughter Ann Eliza, as Kiley on her death certificate, and as Caleb on the death certificate of his daughter Malissa.

“Carey” is probably short for Carroll, since Malissa named one son Caleb and another Carroll.

1850 census of Bath Co., Ky, enumerated 9 Aug, lists as family #364:
Carey, Lourey, 41, farmer, b. Va; Mary, 36; Emily J., 15; Sarah J., 14; Martha J., 8; Malissa, 4; James W., 1. All except Carey born in Ky.

Any of the J’s could be I’s; this census taker formed them identically.

1860 census of Bath Co., Ky, Owingsville P.O., enumerated 4 July, lists on p. 92 as family #674:
Carey Lowery, 50, farmer; Mary, 47; Emily, 25; Sarah, 24; Martha, 18; Malissa, 13; William, 11; Ann, 3.

The birthplace column is blank for the entire page, except the person entered on line 1.

1870 census of Bath Co., Ky, White Sulphur precinct, Marshall P.O., enumerated 13 June, lists on p. 18 as family #175:
Lowry, Mary, 56, Jas W., 20; Ann E., 13; Rody Sexton, 81; Snedager, Susan, 54; Parker, Malissa, 42; Sarah F., 15. All born in Kentucky.

Rody Sexton is Mary’s stepmother. Susan Snedegar may be the mother of Lemuel Snedegar who was married to Mary’s daughter Malissa. Malissa would have been only 24 in 1870, though, with a baby daughter Mary, and still married to Lem, so she does not fit to be the Malissa Parker here.

The preceding household is headed by Presley Sexton, son of Mary’s brother William.