My Lambertson kin left NJ in the early 1830s and went to Brooklyn so I didn't delve too far in NJ records after about 1850. It's possible that James' name was spelled LAMBERSON. I've seen it both ways on the same document. Another problem that I've encountered is the several Lambertson men named Cornelius. It was popular in the family for some reason. Have you found birth or death certificates for the folk that you're researching?