Brian Shivers is to appeal his conviction for the murder of two British soldiers at Massereene Barracks in Co Antrim.
The 46-year-old from Magherafelt in Derry was ordered to serve a minimum of 25 years in prison for killing Sappers Mark Quinsey and Patrick Azimkar in March 2009.
He was also found guilty of six counts of attempted murder and one count of possession of two firearms and ammunition with intent to endanger life.
During his trial, it emerged that Shivers suffers from cystic fibrosis and only has a few years to live.
His legal team claim he was wrongly punished and want an urgent hearing due to his illness.
Solicitor Niall Murphy said: "Mr Shivers was wrongly convicted and punished since no conduct of his could constitute the offences of which he has been convicted.
"We have petitioned the court in our grounds of appeal that the trial judge erred in law by misdirecting himself."
The soldiers were shot by the Real IRA as they collected pizzas outside the Massereene Barracks, hours before they deployed to Afghanistan.
Shivers' co-accused, veteran republican Colin Duffy, was acquitted of all charges.
