Lambert began his activity as a Trotskyist militant before the Second World War when he was a member of the Internationalist Workers Party (POI) led by Molinier. After the war he continued his activism, as a member of the now united French section of the Fourth International, the PCI.
In the PCI he was known as a specialist in trade union matters and rarely took a stand on international issues. When michel pablo, the secretary of the Fourth International, raised the question of entrism sui generis then he took no stand. until his field of opeation in the trade unions was threatened and he then backed the PCI leadership around Bleibtreu and Favre.