Barrister Zafarullah filed a petition in the Lahore Registry of the Supreme Court asking it to direct authorities to send Sarabjit to Britain for treatment.
He also asked the court to free Sarabjit and another 120 death row prisoners as they had been held in prison for a period equivalent to a life sentence.
Zafarullah contended that Sarabjit's condition was very critical and he should be provided with the best medical facilities in Britain.
"The condemned prisoners who have completed the period of a life sentence should be set free and the court should issue an order in this regard," he said.
Another lawyer, Sarfraz Husain, too filed a petition in the Lahore Registry of the apex court, requesting it to send Sarabjit abroad with a medical board of Pakistani and Indian doctors.
He said Sarabjit's case should be referred to the Federal Investigation Agency for an inquiry.
All prison officials and prisoners involved in the incident should be brought to justice without any discrimination, he said.
Husain also urged the apex court to set aside Sarabjit's death sentence and order his repatriation to India.
It could not immediately be ascertained when the petitions would be taken up by the apex court.
Sarabjit, 49, sustained several injuries, including a skull fracture, when six prisoners attacked him in Kot Lakhpat Jail on Friday afternoon.
He was hit on the head with bricks and cut with sharp weapons. He is in a deep coma and on ventilator support in an intensive care unit of Jinnah Hospital.
He was convicted of alleged involvement in a string of bomb attacks in Punjab province that killed 14 people in 1990.
His mercy petitions were rejected by the courts and former President Pervez Musharraf.
The outgoing Pakistan People's Party-led government put off Sarabjit's execution for an indefinite period in 2008.
Sarabjit's family says he is the victim of mistaken identity and had inadvertently strayed across the border in an inebriated state.