*Curwen 1932 pp256-277 describes it thus:
"Hartsop Hall.The former residence of the Bartons of Ormside. It is a little old building say of the 15th century consisting of two blocks at right angles to one another. There is nothing remaining of any note about it."
Hartsop is also briefly mentioned in *Nicolson et al 1777 p407, which may be Curwen's primary source.
There is a coat of arms on the church in Barton hamlet which has been associated with the owners of Hartsop (it does have harts on it), and Hartsop Hall lies within the parish of Barton. It may indeed be that the parish is named for the Bartons of Ormside, and that its peculiarly stretched boundary owes its origins to the distribution of lands owned by this family.
Hartsop Hall. Image from www.english-lakes.com/hartsop.