Lockhart and his new bride Elizabeth/Eliza Small Cook Biggs are on the 1850 Range, Madison Co OH census. The home is a mixure of Biggs and Cook children. The family next appears on the Logan Co IL 1855 State Census.
For 1850 use the transcibed index listing "Eliza Bigs" and/or "Lackhart Bigs".
Lockhart married Peggy Linton in Madison Co OH 8 July 1824 (per recorded license), he next married the widow of Aaron Cook in Madison Co OH on 2 Dec 1849 (per recorded license). Mr. William Small, Elizabeth Catherine Small Cook's father was also living in Madison CO OH at this time.
I will assume that with such a large family of mixed children, life was never 'easy' for Lockhart. According to bio clips Lockhart and Peggy had 5 children. Aaron and Elizabeth (Small) Cook had 5 children. Then Lockhart and Elizabeth had at least three additonal children together. That's a lot of kids to raise and feed, so living in poverty likely was not far from truthful. It would also perhaps account for if and/or why some of the children lived and/or worked outside of the home when able rather than attending school.