He was a member of the New Jersey Legislative Council from 1790 to 1804, and served as vice president from 1801 to 1804.

Lambert was the Acting Governor of New Jersey in 1802 and 1803, serving in 1802 due to a deadlocked vote in the gubernatorial election.

He was elected as a Democratic-Republican to the Ninth United States Congress and Tenth United States Congress, serving in office from March 4, 1805, to March 3, 1809.

What is now the city of Lambertville, New Jersey was named in his honor in 1814 when the community's first post office was established.

He was an avid reader, and was known for owning one of the most esteemed libraries in Hunterdon County, Lambert died near Lambertville, and was interred in Barber's Burying Ground, Delaware Township, Hunterdon County, New Jersey.