Ka kammala wannan magana: A shekara ta 1929, Lambert ya shiga Jam'iyyar Kwaminis a California. Ta yi aiki a matsayin sakataren kungiyar har zuwa tsakiyar 1940s. A cikin wannan muhimmiyar rawa, Lambert ya kasance "na biyu a cikin umurnin jihar CP". Lambert ya kasance mai aiki a cikin manyan yaƙe-yaƙe na farkon shekarun 1930, ciki har da 1933 San Joaquin Valley Cotton Strike da kuma
1934 San Francisco Janar yajin aiki. A lokacin yajin aikin gama gari, an kama ta, tare da dan gwagwarmayar kwaminisanci Ida Rothstein, a kan zargin ɓarna; an wanke matan biyu. Lambert kuma ya shiga cikin siyasa na gida, yana gudana don San Francisco Board of Supervisors a 1931 da 1933 a matsayin dan takarar Jam'iyyar Kwaminis na hukuma, kuma ya lashe kuri'u 10,815 a zaben na 1933. A cikin zaɓen biyu, Lambert ita ce kawai mace mai takara.