Some people show his middle initial as L, and others as P.

She is probably this Betsy Elliott:

1880 census of Bourbon Co., Ky, North Middletown district, enumerated 18 June, lists on p. 14 as household #50:
Elliott, Betsy, 81, widowed, b. Ky Va Va.

The preceding household is headed by Andrew Perrell (or Penell) age 58, and the following one by a widowed Rose Clayson, age 56. There are no other Elliott (or Elliot or Eliot) families in the precinct, although there are 20 other Elliotts in the county, including 4 heads of household. In 1870 the only El(l)iot(t) family in all of Bourbon Co. was a widowed Mary Elliot age 33 with two daughters aged 8 and 5, none of whom are listed in Bourbon Co. under that surname in 1880. So most likely some of the Morgan Co families moved north during the 1870’s.

1850 census of Morgan Co., Ky, p. 163, taken Sep. 28, lists family #1033:
John Lewis Sr., 61; Elizabeth, 50; Gardner, 22; Jackson Petitt, 4. All born in Ky.

I do not know Jackson Petitt’s relationship to John Lewis or Betsy Elliott, but since he was listed with them in both 1850 and 1860 I have attached him as a foster child. See his notes.

1860 census of Morgan Co., Ky, district 1, enumerated 6 June, lists on p. 7 as family #37/36:
John Lewis, 71, farmer; Jackson Pettitt, 15, laborer. The birthplace column is blank for both.

Elizabeth was listed in 1860 as age 60 with their son Gardner.

1870 census of Morgan Co., Ky, Blairs Mill precinct, enumerated 22 July, lists on p. 8 as family #64/61:
Lewis, John Sr., 81, farmer; Elizabeth, 71; Elliott, Henly (m), 3. All born in Ky.