Lithuanian prosecutors say they have been informed about the ruling but refrain from further comments.
"I am informed. I don’t have any details yet but I am aware of this decision," prosecutor Gedgaudas Norkūnas of the Prosecutor General's Office told BNS on Thursday.
The prosecutor could not say whether he would lodge an appeal. "I cannot say anything now. I believe I will shortly get detailed information, and then we'll decide, we'll evaluate the situation," he said.
The Belfast court believes Campbell would be held in inhuman and degrading conditions, according to BBC. The judge drew attention to the fact that Lukiškės Prison in Vilnius is overcrowded and inmates are held in unsanitary conditions.
The Irishman's lawyers brought in a special adviser to the British Home Office and the Council of Europe's Committee for Prevention of Torture as part of their case. Prof Rod Morgan visited Lukiškės Prison in Vilnius and delivered a critical assessment of prison regimes in Lithuania.
Lithuanian prosecutors say Campbell should stand trial for his involvement in an operation to buy and smuggle weapons for the Real IRA from Lithuania.
His brother Michael was jailed for 12 years by a Vilnius court in 2011 after being found guilty of trying to buy weapons for the Real IRA. He was detained in January 2008 after buying weapons from an undercover agent.
Liam Campbell is called one of the leaders of the Real IRA. He was earlier held liable for the Omagh bombing in Northern Ireland in 1998 when 29 people were killed and over 200 injured.
The Real IRA is an Irish republican paramilitary organization which aims to bring about a united Ireland. It is an illegal organization in Ireland, and the Council of Europe considers it to be a terrorist organization.