Lambert himself married Alida, daughter of Cornelis Bicker and Aertge Witsen.
In 1667 he became a 'bewindhebber' or governor of the Dutch East India Company and was made mayor of Amsterdam in 1667, 1668 and 1672.
As mayor, he held a reception for Cosimo III de' Medici at the Van Campen Theatre.
After the death of both brothers and the rise of William III of Orange as stadtholder, Reynst, his brother-in-law Andries de Graeff, his cousins Pieter, Jacob de Graeff and Hans Bontemantel and nine others were dismissed.
[3] Aernout van Overbeke, a 17th-century humorist, described Reynst as the city's greatest "hoerenjager" (literally, whore-hunter), which could mean one who frequented prostitutes or one who prosecuted them.