I inherited a commercial property 2 years ago from my aunt. The neighbor behind us purchased his property from my aunt approximately 10 years ago and has been driving through our parking lot to his property ever since. There are no easements recorded and the neighbors property has convenient access to a state maintained, paved road which adjoins his property. When he purchased the property, he asked for an easment and it was denied by my aunt. I would like to build a new addition to my building and this would involve moving the current parking lot. I told the neighbor that I intend to do this, and asked him to cease driving across my parking lot. He threatens to sue and claims that he has established as easement. I would appreciate any advice.

You need to review the situation with a local real estate attorney. It's quite possible that, by failing to take steps to prevent his driving across the property, your aunt allowed an easement of necessity to be created.

There is no easement of necessity if this person has access to a state road- this is laziness. Also, I do not think enough time has passed for adverse possession easement to occur since your aunt rejected the easement.
fyi from findlaw.com
Under North Carolina law, the prescriptive period for adverse possession is either seven years under color of title or twenty years without color of title.