I have her parents as Hendley Snead (1753-1815) and Mary
Burford.I am a descendant of Lydia's daughter Nancy(aka Nanney)Thomas (1800-1832).Nancy married Aaron Morris (1797-1832).Hendley Snead was a son of Israel Snead (1730-1788)and Johanna Hendley.Israel is listed in Vol.1 "A Roster of
Revolutionary Ancestors of the Daughterd of the American Revolution" (Commemoration of United States of America Bicentennial July 4,1976),page 595.The only proof that I have as to Lydia's parents is the location of her marriage to John Thomas and that they named one of thier sons Hendley Thomas.
I hope this helps you.