Can anyone trace their ancestry to William WILLIAMS, one of the original signatories to the Declaration of Independence?

I've just recently begun tracing my mother's ancestry and remember her always telling us that we were related to him through her grandmother, Lille Dale WILLIAMS of York, PA.
She was born in 1869 to David Gross WILLIAMS of York, PA. and Sarah Ellen MEYERS. She died in 1909.

I know only that William WILLIAMS was born on 8 April 1731 in Lebanon, CT, the son of Solomon WILLIAMS who married as Miss PORTER.
William WILLIAMS was married at the age of 41 (in 1772) to the daughter of a Jonathan TRUMBULL. They are supposed to have had three children: 2 sons and 1 daughter.

I know only that the eldest son's name was
Solomon (after his grandfather) and that he died in NY in 1810. William WILLIAMS is said to have been devestated by his son's death and passed away on 2 August 1811 at the age of 81.

If anyone can help me establish a link to David Gross WILLIAMS and daughter Lillie Dale WILLIAMS, I would be eternally grateful.
My email is rodagreen@yahoo.com.