Update: I wouldn't put too much stock in the version of this family's line I posted last year. The more I've researched them, the more confusing it gets. It may be that the correct line is --
Phillip Lambert m. Amy Pearsall > Phillip Lambert m. Mary Evans > Pearsall Lambert m. Mary Rice > Pearsall Lambert m. Gincy Harper
With original Phillip and Amy also having a son whom they named Pearsall who also may have had descendants named Pearsall.
I visited the Craven Co., N.C. library earlier this year to find records to help with any of this. Unfortunately, their records on the 1700s in their own county were virtually worthless. (Though the person on duty talked my ears off with the results of a online search I could have done from my own computer that turned up Lamberts and Pearsalls all over the place, but not in North Carolina, Virginia or Ohio, those being the relevant places!)