Answer by taking a quote from the following article:

Born and raised in Mbewuleni, Cape Province, Union of South Africa, Mbeki is one of four children of Epainette and Govan Mbeki. The economist Moeletsi Mbeki is one of his brothers. His father was a stalwart of the African National Congress (ANC) and the South African Communist Party. He is a native Xhosa speaker.

Together with Oliver Tambo, Mbeki left London for Lusaka in April 1971 to take up the position of assistant secretary of the ANC's Revolutionary Council (RC). This was the first time in nine years that Mbeki was setting foot on African soil. The aim of the RC at this time was to bridge an ever-widening gap between the ANC in exile and the people back home. In Lusaka, Mbeki was housed in a secret location in Makeni, south-west of the city. Later, Mbeki moved over to work in the ANC's propaganda section. But he continued to attend RC meetings. Four months after his arrival in Lusaka, Mbeki travelled to Beichlingen to deliver a speech on behalf of the ANC's Executive Committee at the YSS summer school. This was a turning point in Mbeki's life as it was the first time he spoke on behalf of the ANC as opposed to the ANC Youth League.  In December 1972, Mbeki joined Tambo at Heathrow Airport to meet Mangosuthu Buthelezi to discuss mass resistance to apartheid. Mbeki is credited with facilitating the establishment of Inkatha - it was his responsibility to nurture the relationship between Buthelezi and the ANC. Mbeki was deployed to Botswana in 1973 to facilitate the development of an internal underground.  Mbeki's life took a significant turn on 23 November 1974 when he married Zanele Dlamini. The wedding ceremony took place at Farnham Castle, the residence of Zanele's sister Edith and her husband, Wilfred Grenville-Grey. Adelaide Tambo and Mendi Msimang stood in loco-parentis for Mbeki while Essop Pahad was Mbeki's best man. The wedding, according to ANC rules, had to be approved by the organisation - a rule that applied to all permanently deployed members of the ANC.

What was his mission in Lusaka?
Mbeki travelled to Beichlingen to deliver a speech on behalf of the ANC's Executive Committee at the YSS summer school.