The Gupta family will on Friday morning file responding court papers at the High Court in Pretoria t.
They urged the SA Human Rights Commission (SAHRC) to investigate allegations that health and related rights of inmates were being violated.
"On May 28, [the] group of organisations wrote to the SAHRC to request that it urgently investigate the state of health and health care service provision at Lindela... [and] requested a response from the SAHRC by June 11."
The four rights groups are Médecins Sans Frontie'res, Section27, Lawyers for Human Rights, and People against Suffering, Oppression and Poverty.
They said in a statement: "These abuses have been documented throughout Lindela's existence. Moreover, what we know about Lindela is shocking, but our lack of knowledge of what occurs behind its walls is cause for even greater concern."
The facility operated "in secrecy and with impunity", the groups claimed.
SAHRC spokesman Vincent Moaga confirmed the request for an investigation had been received.
The commission had visited the centre, and a letter to the groups was being dispatched to invite them to meet its chairman.
"We have been working on this, we are now waiting for the (home affairs) minister's response."
Last week Tuesday, Moaga said the SAHRC asked the home affairs department to come up with urgent and meaningful measures to put an end to the ill treatment of refugees and asylum seekers.
"The rights of non-nationals are specifically protected in national law and in international human rights agreements," Moaga said.
"This group is particularly vulnerable and the state is obliged to take appropriate steps to ensure the basic rights [of] this group are adequately protected." - Sapa