The Dorothy Fairfax descent I believe you are looking for would be:
Ferdinando, second Lord Fairfax, m. 1607 to Mary, daughter of Edmund Lord Sheffield, Earl of Mulgrave, and President of the North. Lord Fedinando died at Denton, Yorkshire. on March 13th, 1647.
Their second child was Ellen born at Toulston on Feb. 10, 1611. She married Sir William Selby of Twizell, by whom she had one child, Dorothy, wife of Sir William Foster of Bamburgh. I don’t have later generations of this family.
My source is a manuscript by Charles Fairfax of Menston, noted antiquary and genealogist, and younger brother of Ferdinando.
Hope this helps.