William Parker Lucas - William Lucas had a brother named Parker Lucas

@William Lucas
William Lucas and Parker Lucas were brothers.
There are records that indicate this fact in the "Southern Campaigns American Revolution Pension Statements and Rosters."
Here is a partial record:
"Pension Application of William Lucas R6507 VA Transcribed and annotated by C. Leon Harris. Revised 17 Dec 2014."

"Logan County Va. November the 1st day 1834"

"We the undersigned Justices of the peace for the County of Logan in the State of Virginia Do hereby certify that at the request of
William Lucas who, from old age and infirmity, is unable to attend at the Courthouse of said County; We attended at the house of his son John Lucas, where he now lives, and the said William Lucas, being duely Sworn, in form of Law, made the following, declaration, in order to obtain, the benefit of an Act passed by Congress on the 7 day of June 1832. That he was drafted, in the year 1772 to go on a tour of Service; to protect the frontier of Virginia, a gainst the Indians, and also in 1773 and a gain in 1777 he was drafted, for the same Service, & was stationed at Farleys fort on New river for 3 months; and in 1778 he was Stationed at Woods fort for 3 months; He was shortly after drafted into the Virginia Militia, & served a tour of three months, in the Regiment Commanded by Colonel Shelby; in the Company of Captain Abraham Trigg, was with the army under Gen’l. Campbell in Carolina, at the end of this tour He enlisted into the regiment Commanded by his neighbour Col. Preston, and served a tour of three months, in the Company of James Burns; Lieut Snidow, when he was discharged.

He also enlisted with his brothers in hiring substitutes, as the Law required; and alltho’ his brother in Giles County [Parker Lucas], in better circumstances has received a pension, he has received nothing in payment for his services, whatever; He is now 84 years of

Age, and very infirm, and poor; and certainly well entitled to his Countrys aid; in the time of his great need; and utter inability to help himself–: He relinquishes every other Claim except the present, to any pension; & his name is on no pension Roll whatever in any State– William hisXmark Lucas

Sworn to, and subscribed before us this 1st day of November 1834
[signed] Anthony Lawson J.P. Nath’l. Mullins JP"

William Lucas married Elizabeth Price and Parker Lucas married Margaret Price.
Parker Lucas [S8868]; William Lucas [R6507]. Different people. Both sons of Charles Lucas.
Image of Giles history posted in sources.