Not exactly. Lord Dunmore’s War was an Indian conflict in western Virginia along the Ohio River. Many of the participants on the Virginia side lined up against each other after Lexington and Concord. For example, Lord Dunmore, a rebel earlier during the ‘45, led the British forces in Norfolk against the Patriots at the Battle of Great Bridge in 1775. While Daniel Morgan, a distinguished Patriot commander at Quebec, Saratoga, etc, fought for Dunmore in the Virginia militia in Lord Dunmore’s War.
You just named one of my all time favorites. Daniel Morgan is an outstanding Revolutionary hero and the Battle of Cowpens was, IMO, the REAL blockbuster for Cornwallis when he lost Tarleton’s Army. I would suggest reading anything and everything on Daniel Morgan. He and his Virginia sharpshooters were everywhere from Quebec, through Saratoga, to the battles in the south.