In the early 1600's he served under Willem Haultain and Jacob van Heemskerk and was present as Rear Admiral at the Battle of Gibraltar. He was active against the Dunkirk corsairs and in 1605 managed to defeat and capture the Dunkirk admiral Adriaan Dirksen.
From 1616 to 1624 he was mostly active in the Mediterranean to protect Dutch merchants from the Barbary pirates and in 1618 teamed up with the Spanish to defeat the Algerian corsair fleet.
In 1622 he negotiated a peace agreement with the pasha of Algiers to leave Dutch merchant shipping unmolested, after this treaty was broken by the Algerians Lambert was sent to take punitive action against the Barbary pirates and through harsh negotiations managed to force the Algerians to set hundreds of Christian slaves free.
After his death ,having served the admiralty of Rotterdam for more than forty years, he was given a grave memorial in the St Laurens church Rotterdam.
The inscription on the epitaph reads:
Hier leidt in 't graf een held manhaft
Mooy Lambert Hendrikszoon
Die in zijn tijd tot Spanjaars spijt
Haar trots heeft 't hoofd geboon
Zijn deftigheid was ook verbreid
Onder de Turkse natie
Die hij dikwijls met zijn metaal
Verwon in korten spacie