Power utility Eskom on Wednesday called on consumers to switch off geysers, pool pumps and all non-e.
Lambert, who was affectionately known as "Aunt Ellen" among party members, died at the age of 78.
She joined the ANC in 1953 and was one of the Freedom Charter volunteers. At her youthful stage, she worked with ANC leaders including Walter Sisulu, Ahmed Kathrada and many others.
Lambert operated underground during the banning of the ANC and was constantly harassed by police.
During the 1980s, Lambert worked tirelessly for the formation of the United Democratic Front, leading major campaigns opposing the apartheid tri-cameral parliament.
After the unbanning of the ANC, she was among those who established the first ANC branches in Reiger Park, Actonville, and Eldorado Park. Among the mourners were Gauteng Premier Nomvula Mokonyane and Minister for Women, Children and People with Disabilities Lulu Xingwana.