Lauren's brother was Cornelius Jansen Kortright who died in 1727. They were sons of Jan Bastiassen who came over 1663 with his 2 sons. C.J. Kortright married in 1665 Metje, daughter of Bastiaen Elyessen (Metje Cornelis). His children were not baptised in Kingston, Ulster County, New York. The patterns of baptisms and marriages indicates that he and his family may have resided in New Amsterdam. There is very little information on this family.
I believe they were married at the Hurley DRC which was formed in 1708. This was in the town of Hurley on the Esopus Creek in Ulster Co., NY.
I've seen the name of Lawrence's birth place given in various ways. It was somewhere in Holland/The Netherlands. The same for his wife.