Lambert gained a BA in Modern Languages in 1971 from University College, Cardiff, before taking a Postgraduate Certificate in Education (PGCE) from St Pauls' College (Francis Close Hall), Cheltenham (now the University of Gloucestershire) and gaining an ADB (Ed.)

She then worked as a secondary school teacher in Waltham Forest, East London,[4] first from 1972–78, then from 1985–89 and finally between 1993 and 1999.

[6] Lambert was first elected to the European Parliament in 1999 from the London Region, winning 87,545 votes (7.7% share).

As a Member of the European Parliament, she is or has been a member or substitute of the Employment and Social Affairs Committee, the Civil Liberties, Justice and Home Affairs Committee, the Subcommittee on Human Rights, the Intergroup on Disability and Gay and Lesbian Rights[4] and Delegations to South Asia, Afghanistan, Japan and India.

She was Vice-President of the Greens/European Free Alliance Group of MEPs from 2002 to 2007, in which she is the Spokesperson on Asylum and Refugees.