I am researching the same Joseph Lowery Alexander, and I find your information very interesting.I don't have a Nancy Alexander in my database and suspect that she might be the granddaughter to Joseph Lowery Alexander, just not sure which of Joseph's sons she belongs.I have that Joseph had William b. 1771, Samual b. 1773, Robert b. 1775 and John Piper b. 1793.Another possibility is that Nancy is the daughter of Joseph Lowery Alexander and I don't have her information.
I very much would appreciate you sharing any information that you might find on this connection.