Lambert took an active part in the teachings of rue Monsigny, collaborating with the newspaper Le Globe and during the split that occurred in the Saint-Simonian family, he chose to side with Enfantin.

From his refuge at Ménilmontant, he appeared as trial counsel for one of the accused and produced an incisive and mocking speech which elicited a number of observations from the presiding judge.

A member of the Higher Council for Education, Lambert participated in the development of all reforms of the school system in close liaison with Minister Ethem Bey.

During his time in Egypt, Lambert attentively studied the work of French engineer, Jacques-Marie Le Père, who at the end of the 18th century proposed a canal to traverse the Suez Isthmus.

In 1851, Lambert settled in Paris and devoted his leisure to questions of philosophy: he published a very curious study about the Trinity which was a great success when it appeared in La Revue philosophique et religieuse.