"It is over violation of the right not to be tortured, violation of the right to a fair trial... eight-year delay of the procedure, illegal death penalty, illegal detention," Zegveld said.
Last month, Alhajouj also filed a lawsuit in France against Muammar Gaddafi, the Libyan leader, accusing him of torture.
Zegveld said her client was seeking international recognition that he was innocent.
"He has been pardoned and sent to Bulgaria. But the verdict stays and someone needs to scratch out this verdict and a human rights committee has the right to do that at an international level," she said.
"The UN committee will decide whether Libya has violated the international human rights treaty... It works like an international court but in a more loose manner in a sense that it's not a binding decision."
Last year, Libya commuted the medics' death sentences to life imprisonment after the 460 HIV victims' families were paid $1m each in a settlement financed by an international fund.
Georgi Parvanov, Bulgaria's president, pardoned the six after they arrived in Sofia in July.
Zegveld has said Alhajouj delayed filing the complaint against Libya under political pressure from European politicians who tried to convince him not to press charges to avoid harming the EU's improving ties with Tripoli.
The return of the medics to Bulgaria ended what critics called a human rights scandal and allowed the long-isolated country to complete a process of normalising ties with the West.
The six have said that before their release they were made to sign an agreement that they would not start any legal procedures against Libya.
Nine Libyan policemen and a doctor were acquitted of torturing the medics by a Libyan court.
International scientists say they have shown the HIV epidemic began in Libya before the foreign medical staff arrived.