Published Thursday, 15 August 2013
Liam Campbell was arrested in Co Armagh in 2009. (© UTV)
Lawyers for the Baltic state wanted the UK's highest court to overturn two previous rulings which blocked Liam Campbell's transfer.
But judges at the Supreme Court in London have refused permission to appeal, deciding no point of law of general public importance had been raised.
The verdict reached two weeks ago means Campbell, one of the men held liable for the Omagh bombing in a landmark civil action, is no longer subject to any proceedings in this jurisdiction.
He has already had bail conditions including electronic tagging and a prohibition on living outside Northern Ireland lifted.
The 50-year-old, of Upper Faughart, Dundalk, Co Louth spent nearly four years behind bars as Lithuanian authorities sought to have him face charges linked to an operation to acquire guns, ammunition and explosives and ship them into Ireland.
In February, a panel of High Court judges backed an earlier ruling refusing their extradition request.
They decided that he would be held in inhuman and degrading conditions.
Lithuania's legal representatives then attempted to mount a further challenge to that determination.
But a Supreme Court spokesman confirmed on Thursday their application was rejected on 31 July.
Campbell had been released on bail conditions which included the lodging of £75,000 in cash sureties.
It is understood those sureties are no longer in force. Although a further challenge could still be taken to the European Court of Human Rights, legal sources said this was highly unlikely.
Extradition proceedings first began when Campbell 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 ruling followed a lawsuit brought by relatives of some of the 29 people killed in the August 1998 atrocity.
According to the judge at the time, there was cogent evidence that Campbell was a member of the Real IRA's Army Council.
Earlier this year two other men, Dundalk-based builder and publican Colm Murphy and Seamus Daly, from Cullaville, Co Monaghan, were held liable following a civil retrial.
© UTV News