The pair are suspected of involvement along with Abdelbaset al Megrahi - the only person convicted over the 1988 atrocity in which 270 people died.
Scottish prosecutors said they want the suspects to be interviewed by police.
The Crown Office has not confirmed the suspects' identities, but they have been named in reports as Abu Agila Mas'ud and Abdullah al-Senoussi.
Revd John Mosey, whose daughter Helga was killed in the bomb, told Premier he had met al-Senoussi.
"He's not a nice man at all," he said about the man who's on death row in Libya at the moment for his role in the regime of Colonel Gaddafi.
Revd Mosey added: "If you were on death row, waiting to be executed? I think I would be prepared to confess anything to exchange death row in Libya for a central heated cell with Sky TV in Scotland and a Scottish trial.
"I've got some very serious questions about Libya.
"How can one believe anything that comes out of Libya when it's in such chaos.
"Scottish people and Americans are dealing with an unelected government in Tripoli."
Both of the newly-identified suspects were reportedly imprisoned in Libya after the 2011 fall of Colonel Muammar Gaddafi, and Senoussi has been sentenced to death. Senoussi is said to have been Gaddafi's brother in law and head of intelligence.
The crimes they have been charged with in Libya are not related to the Lockerbie bombing.
The Pan Am flight was on its way from London to New York when it exploded above Lockerbie, in southern Scotland, on the evening of December 21 1988, killing everyone on board and 11 people on the ground.
Megrahi was found guilty of mass murder following a trial at Camp Zeist in the Netherlands in 2001 and was jailed for life with a minimum term of 27 years.
Last year, exactly 26 years on from the atrocity, the Lord Advocate led a delegation of Scottish law officers who attended a memorial at the Arlington cemetery in Washington.
Mr Mulholland, who addressed the service, said no Crown Office investigator or prosecutor has raised a concern about the evidence in the case and he vowed to track down Megrahi's accomplices.
He has previously said the idea that Megrahi acted alone was ''risible''.
The investigation into the bombing remains a joint one between US and Scottish prosecutors, Police Scotland and the FBI.
A Crown Office spokesman said: ''The Lord Advocate and the US attorney general have recently agreed that there is a proper basis in law in Scotland and the United States to entitle Scottish and US investigators to treat two Libyans as suspects in the continuing investigation into the bombing of flight Pan Am 103 over Lockerbie.
''The Lord Advocate has therefore issued an international letter of request to the Libyan attorney general in Tripoli which identifies the two Libyans as suspects in the bombing of flight Pan Am 103.
''The Lord Advocate and the US attorney general are seeking the assistance of the Libyan judicial authorities for Scottish police officers and the FBI to interview the two named suspects in Tripoli.
''The two individuals are suspected of involvement, along with Abdelbaset Ali Mohmed al-Megrahi, in the bombing of flight Pan Am 103 in December 1988 and the murder of 270 people.''
Premier's Hannah Tooley speaking to Revd John Mosey: