Addressing a youth league economic freedom seminar last night at the University of Cape Town, a stronghold of the DA, Lamola said Vavi should never be intimated by a "mouthpiece of monopoly capital", an indirect reference to DA leader Helen Zille, who recently emerged as a fierce Cosatu critic.
Zille had accused Vavi of harbouring ambitions to lead the ANC.
Lamola, who has effectively become the new spokesman for the "economic freedom fighters" following the expulsion of Julius Malema, said Vavi must never apologise for aspiring to lead the ANC.
He said Vavi, like the late Hani, was a selfless leader who was not driven by the desire to enrich himself at the expense of the working class.
"It is the responsibility of the youth league to defend comrade Vavi. We are inspired by comrade Vavi and we will never be told by Helen Zille who comrade Vavi is," said Lamola.
"In our own eyes, when we see comrade Vavi we see comrade Hani, he is the modern- day Chris Hani and is selfless in the struggle for the workers ... he has never pursued self interest or self enrichment.
"Comrade Vavi must never apologise for having an ambition to become a leader of the ANC because former leaders of Cosatu and many trade unions led the ANC," said Lamola in reference to leaders such as Cyril Ramaphosa and ANC deputy president Kgalema Motlanthe, who honed their leadership skills in the labour movement before taking leadership positions in the ANC.
Vavi is said to be part of the powerful block that wants a leadership change in the ANC, and the youth league is reportedly planning to nominate him for a position of party national chairman.
"Comrade Vavi must never apologise for having such an ambition because that is where he is going, he will one day lead the ANC, he will one day lead the SACP," he said.
Lamola also hit back at Young Communist League (YCL) general secretary Buti Manamela, who on Tuesday told a Workers Day rally in Durban that the youth league had been taken over by "Superman and Batman" politicians whose interests were positions of power.
Lamola branded Manamela a "coward" who has suddenly found the courage to speak out against the youth league because Malema had been expelled from the ANC.
"The YCL is not an autonomous structure of the SACP, and that's why comrade Buti will never understand why the (ANC) youth league behaves the way it does ... he will never understand this because the YCL is a conveyer belt of messages from the SACP," he said.
Lamola challenged Manamela to directly approach the leadership of the ANCYL to raise his concerns.
"What he said is grandstanding and political opportunism ... he never had the courage to say these things before comrade Julius was expelled ..." said Lamola.