Laurens arrived in the New Amsterdam colony around 1640 from Amsterdam, Holland. He was a noted sea captain of the West India Company, and involved in numerous lawsuits as revealed in old court records. He became heavily involved in the maritime shipping industry, and was a prominent citizen involved in early colonial politics.

On 18 Apr 1657, in New Amsterdam, Kings County, New York, Laurens was granted the Great Burgher Right. "We, Burgomasters of the City of Amsterdam in New Netherland, hereby certify and declare, that Lourens Cornelisen van Wel has asked for and received from us the Great Burgher Right and the benefits thereof, has taken the Burghers oath and paid the fees to the Treasurer." This meant he was a citizen of the highest standing.