Kenneth, to the best of my knowledge Susanna Lucas and Robert Lucas were not related.However, a granddaughter of John Rush/Susanna Lucas and a grandson of Robert Lucas/Elizabeth Cowgill were md. in 1729/30.Mary Darke md. Edward Lucas, Jr.; the Darke and Lucas families were neighbors in Bucks Co., PA.
To answer your question as to the names of the parents:
Susanna Lucas was christened 29 Jan 1627/28 at Guilsborough. Northampton, the daughter of John Lucas/Ann ____.Family Search states John Lucas was the son of James Lucas/Hannah Bowman.
Susanna Lucas was md. 8 June 1648 at Banbury, Horton, Oxfordshire to John Rush, who was christened 20 May 1623 at Boreham, Oxfordshire, and died May 1699 at Byberry, Phildelphia Co., PA.
John Rush was commander of a troop of horse in Cromwell's army.John and Susanna Rush came to PA in l683 with their seven children and several grandchildren.They settled 13 miles from Philadelphia in Byberry PA on a tract of land adjoining that of son-in-law John Hart.John and Susanna had a total of 10 children.Their youngest daughter Jane Rush b 27 Dec 1673/4 md. John Darke, the son of William Darke/Alis(Alice) Butcher, originally from Rysing, Camden, County Gloster, England.It was John Darke/Jane Rush's daughter Mary, b. 1709 who md. Edward Lucas, Jr., the son of Edward Lucas/Bridget Scott.
Later I will send you some info re Robert Lucas/Elizabeth Cowgill from Deverill Longbridge, Wiltshire to Bucks Co., PA.
Kenneth, I am a descendant of Edward Lucas, Jr./Mary Darke thru their son Robert (l740-1781) who md. Sarah Dungan and moved to the area now known as the State of Tennessee.I am very interested to learn your connection.