Selma has given some excellent tips, and is a Virginia researcher.
I have one thing to add (as a non-VA researcher):
Since you have done quite a bit of research from 1790 forward, you have probably already come across these resources. Still worth a mention here.
1. Re-check existing records
a) at the LVA:
Burned County Notes: http://tinyurl.com/9horm5
b) Lipscomb family vitals.
It is important to know Henry's 'fit' in the Lipscomb family genealogy AND associated (collateral) surnames.
Was Henry's father named John?
He died between 1775-1779. His wife survived him.
Mrs. John Lipscomb appears to have inherited from her father (a Madison).
Could her son, Henry, have inherited from his Madison grandparents?
(More surnames and possibilities.)
Click on the pages to view from the left navigation pane. (John, p. 423)