Apparently, James Patton Lawson had a life-long relationship with Lula Ann Barner, and fathered at least three of her seven children. Lula remained single her entire life and Ollie was probably sent to live with JP and Nancy Lawson so that there weren't so many mouths to feed in the Barner household and Ollie could help Nancy with her younger children. In 1880 she is living with Lula and in 1900 she is living with JP and Nancy.
As for the other four of Lula's seven children, it is said two were fathered by Albert Templeton, the brother-in-law of Nancy's younger sister Sarah, who married John Templeton. One is said to be fathered by a Manis, no first name mentioned. No father identified for her last child.