I have never researched in Virginia courts, but from what I have been able to gather from a browse on the internet, suits such as you describe, if the Probate court validated the will, but a disatisfied party appealed, would have been appealed to Circuit Court. If the appeal was based on some techicality of law, it would have been heard as a "Lawsuit." Useful records associated with cases at law include declarations, writs and minute books.
If the case rested on principles of fairness - "Equity" - the petition would have been heard in Chancery - which was the same Judge as Circuit Court, but acting as a Chancellor for Causes in Equity. Useful documents associated with causes in equity include petitions, orders and minutes.
A case like this probably also included sworn written testimony, called Interrogatories, from witnesses who could not appear in court in person.
I looked at the Library of Virginia webpage - they do not list any circuit court records for Lunenburg, but they say they are still preparing web-based inventories of their holdings for many counties.
I'd write them and ask what Circuit Court records they have for Lunenburg for the 1820s.
The case may even have reached the Virginia Supreme Court of Appeals.