Mr Justice Burgess refused to order Liam Campbell's transfer because he was likely to be held in inhuman and degrading conditions.
Campbell, 49, of Upper Faughart, Dundalk, is wanted in the Baltic state over allegations he was part of an operation to acquire guns, ammunition and explosives from there and ship them into Ireland for dissident republicans.
His lawyers resisted extradition proceedings by arguing that it would breach his human rights.
They brought in a special adviser to the British Home Office and the Council of Europe's Committee for the Prevention of Torture as part of their case.
Professor Rod Morgan visited Lukiskes Jail in Vilnius and delivered a critical assessment of prison regimes in Lithuania.
Campbell's case centred on an argument that extradition would breach his right to freedom from torture, inhuman or degrading treatment or punishment under European law.
Mr Justice Burgess pointed out that reports of human rights violations were not in themselves evidence that a person would be at risk.
The determining factor was whether violations were systemic and the extent to which an individual could be specifically vulnerable to them.
After referring to an earlier judgment which detailed severely overcrowded and unsanitary conditions at Lukiskes Prison, the judge said he was satisfied that extraditing Campbell to Lithuania would expose him to a real risk of inhuman and degrading treatment by reason of the jail conditions.
His decision is expected to be appealed by the Lithuanian authorities.
Campbell remains in custody pending a bail application which could take place this week.
He has been in prison since he was arrested after crossing the border into south Armagh in May 2009.
A month later he was found liable, along with convicted Real IRA leader Michael McKevitt, for the Omagh bombing.
That verdict followed a landmark civil action brought by relatives of some of the 29 people killed in the August 1998 atrocity.
Mr Justice Morgan, now the Lord Chief Justice Sir Declan Morgan, said at the time there was cogent evidence that Liam Campbell was a member of the Real IRA's Army Council.
Two other men originally held responsible, Dundalk-based builder and publican Colm Murphy and Seamus Daly, from Culaville, Co Monaghan, are currently facing a civil retrial after the findings against them were overturned on appeal.
Campbell's lawyer, Kevin Winters, confirmed that he will now be seeking his client's release from custody.
He said: "We welcome the courts ruling coming as it does some three years after the initial extradition warrant was served, one of the longest periods that anyone has spent in custody on proceedings of this nature.
"We have concerns about that and to that end we will continue to highlight it in the bail application."