Lambert was a member of several bands in the 1960s, including The Syndicate, The Chains, and Friday's Chyld / Fire. In 1972 he joined the King-Earl Boogie Band, an outfit formed by two former members of Mungo Jerry. They had briefly fired Ray Dorset from Mungo Jerry with the intention of replacing him on guitar and vocals with Lambert, until Dorset was reinstated by management and record company.
The King-Earl Boogie Band's debut album was produced by Dave Cousins, a move which led to Lambert playing on Cousins' solo album Two Weeks Last Summer.
Lambert then joined Cousins in The Strawbs on guitar and vocals later in 1972, replacing Tony Hooper, and playing on the album Bursting at the Seams, which reached number two in the UK Albums Chart, the album including Lambert's song "The Winter and the Summer". In 1973 Lambert and founding member Dave Cousins started a new lineup of the band that continued until they split up in 1978. He susbsequently worked as a songwriter in partnership with Chas Cronk, recorded as a solo artist and spent time working as a ski instructor. Lambert rejoined The Strawbs in the 1980s and still plays with the band on occasion. In 2006 he was part of a briefly-reformed Fire.