"The correspondence did not produce any result," Viktoras Kazys, chairman of the panel of judges, said at the hearing on Wednesday.
The court is hearing a plea filed by Irish citizen Michael Campbell who has been sentenced to 12 years in prison for assisting a terrorist group, possession of arms, and attempted arms smuggling.
In March 2012, the Court of Appeals ruled to interrogate the convict's brother Liam Campbell and other defendant Brendan McGuigan. They are litigating in Northern Ireland and Ireland for extradition to Lithuania.
In Kazys' words, the correspondence on interrogation of the two individuals was started in spring of 2012 but, after scores of letters, Ireland said this January it was not sure whether it would be able to satisfy the request for legal assistance. British authorities said the interrogation would be decided after the extradition process is over.
"We cannot force English or Irish institutions to take any action. If they don't, they don't. This indicates their attitude towards our requests," Kazys said.
The judge said the next court hearing will take place on June 27 to decide whether the case should be closed due to failure to receive the requested data.
Michael Campbell, 40, was brought to the courtroom on Wednesday in chains. He said he wants the proceedings to go faster.
"I would like the court to move on cause it seems to me that there is no information coming from establishments either in Ireland or in England," the Irish citizen told the Vilnius court.
His lawyer Ingrida Botyrienė said that the case should be heard with the existing evidence, should no information be received within a month.
"Considering the content of the correspondence, it is clear that no actions are taken and it seems that none will be taken. This is something we have to regretfully admit," said the lawyer.
Michael Campbell was detained in Vilnius in January 2008 after buying arms from an undercover secret agent.
Lithuanian prosecutors have cited classified witnesses as saying Campbell inquired about the amount of explosives needed to blow up a governmental automobile and said he would use the arms against humans.
Campbell pleads not guilty, saying he was provoked by British security agents.
Lithuanian prosecutors say the arms purchase operation was organized by his brother Liam Campbell who is titled one of the leaders of the Real Irish Republican Army, a paramilitary organization that opposes British rule of Northern Ireland.
Courts of Northern Ireland have refused to hand over Liam Campbell to Lithuania due to poor imprisonment conditions in Lukiškės Prison in central Vilnius. However, Lithuanian authorities hope the London-based Supreme Court will order to review the rulings.
An Irish court has also refused to extradite Brandan McGuigan to Lithuania, but the ruling can still be protested.
Both suspects are currently at large.
"The (extradition) processes are not over yet, the process is still underway until final decisions are made," prosecutor Gedgaudas Norkūnas told Vilnius court.