Lambert, who works for the Ministry of Health in Pretoria, South Africa, is currently a visiting research associate at the Five College Women's Studies Research Center. At the research center, she is writing a book on the history and international law aspects of the World Health Organization's Framework Convention on Tobacco Control (FCTC). Lambert was a key figure in helping draft this crucial international health treaty.
Lambert's career at the Ministry of Health has been marked with multiple landmark successes in the realm of equal rights advocacy. She has worked on projects concerning affordable medicines and treatment, women's reproductive rights, and fighting discrimination against women. Lambert is also responsible for drafting, as a member of a three-person drafting group, legal arguments for the inclusion of the right to equality on the basis of sexual orientation, in the final Constitution of South Africa. As a result of Lambert's work, South Africa has become the first country to protect the rights of LGBTQ citizens in its constitution.