[1] Lambert served under Willem de Zoete and Jacob van Heemskerk, and was present as a rear admiral at the battle of Gibraltar.
From 1616 to 1624, Lambert was mostly active in the Mediterranean to protect Dutch merchants from the Barbary pirates, and fighting in the Dutch–Barbary war.
In May 1618, he fought at Gibraltar against a Spanish fleet under Miguel de Vidazábal, in an ultimately inconclusive battle.
In June of the same year, he teamed up with Vidazábal himself to defeat an Algerian corsair fleet, sinking or capturing half of the enemy ships.
In 1622, he negotiated a peace agreement with the Pasha of Algiers to leave Dutch merchant shipping unmolested.