He supervised construction of the gas chambers for the Action T4 euthanasia program at Hartheim, Sonnenstein, Bernburg and Hadamar, and then at Sobibór and Treblinka extermination camps during Operation Reinhard.

He specialized in building larger gas chambers that killed more people than previous efforts in the extermination program.

Late in 1939, the Action T4 program tried to recruit Lambert, who had been recommended by the local office of the German Labour Front.

[2] After T4's termination, Lambert was posted to Operation Reinhard in Lublin reservation for the purpose of bricklaying assignments which constructed the gas chambers in Sobibór and Treblinka extermination camps.

With the help of Ukrainian volunteers, and condemned Jewish prisoners, Lambert constructed solid gassing facilities at Sobibor and Treblinka: "Using his expert knowledge about gassing installations, Lambert was able rapidly to complete all work on the big gas house [in Treblinka]".

[2] During his testimony at the Sobibór trial in Hagen, Germany (whose lead defendant was Kurt Bolender), lasting from 6 September 1965 until 20 December 1966, Lambert stated: I was in the extermination camp of Jews for about two to three weeks.

Reportedly, Lambert attempted to remain an uninvolved expert devoted solely to his work and not interested in the conditions which surrounded it.

According to one survivor, Jankiel Wiernik, Lambert avoided looking at dead bodies and treated his Jewish workers in a professional manner.

[5][6]At the conclusion of Operation Reinhard, Lambert was posted to Trieste, where he continued installing cremation facilities at the concentration camp Risiera di San Sabba.

At the First Treblinka Trial in 1965, Lambert was tried for the first time and sentenced to four years' imprisonment for aiding and abetting the murder of at least 300,000 people.