Six immediate members of Abdelbaset al-Megrahi's family have joined forces with a number of British relatives of those who died in the atrocity to seek a third appeal against his conviction in the Scottish courts, a press conference in Glasgow heard.
They are today lodging an application with the Scottish Criminal Cases Review Commission (SCCRC), the body which reviews alleged miscarriages of justice in criminal cases and has the power to refer a case back to the High Court.
Megrahi was the sole person found guilty of the bombing of Pan Am flight 103 over Scotland on December 21 1988, in which 270 people were killed.
The Libyan abandoned a second appeal against conviction in 2009 after being diagnosed with terminal prostate cancer.
He was later released from jail by the Scottish Government on compassionate grounds and died protesting his innocence in May 2012.
Solicitor Aamer Anwar said that, more than a quarter of a century after the atrocity, "the truth remains elusive".
Speaking in Glasgow, he said: "The case being lodged this morning seeks to overturn the conviction of Abdelbaset al-Megrahi for murder."
The solicitor said the three volumes of papers which form the basis of the new application will be delivered to the SCCRC later today.
He has been instructed by 24 British relatives of victims and "six immediate family members" of Megrahi who, for safety reasons, are not being identified.
Over the 25 years since the bombing and Megrahi's subsequent conviction, there have been many legal twists and turns in the case which have brought his family to this point.
Some of the victims' families believe Megrahi was rightly found guilty, and prosecutors at the Crown Office in Scotland insist they do not fear scrutiny of the conviction and would "rigorously" defend it.
But others, including a group of campaigning British relatives, argue that the Libyan was wrongly put behind bars and that the truth about who murdered their loved ones remains elusive.
Megrahi was found guilty of mass murder following a trial at Camp Zeist in the Netherlands in 2001 and jailed for life with a minimum term of 27 years behind bars. He lost his first appeal in 2002.
The following year, he applied to the SCCRC for a review of his conviction. A £1.1 million investigation by the body led to a finding in June 2007 of six grounds where it believed a miscarriage of justice may have occurred.
This decision opened the door to Megrahi's second appeal against his conviction. Although a number of hearings had already been held before senior appeal judges, he dropped his appeal two days before being released from prison in August 2009.
Despite the guilty verdict and Megrahi's decision to drop the appeal, campaigners and families of victims are still dealing with the impact and it has been known for some time that a number of them were considering another appeal.
Last month, it emerged that a new application for the conviction to be looked at again was soon to be handed to the SCCRC by campaigner Jim Swire, representing more than 20 British relatives of bombing victims.
Dr Swire, whose 23-year-old daughter Flora died in the bombing, has long held the view that Megrahi was not guilty of the atrocity.
The fact that Megrahi's own family have now chosen to take forward a fresh appeal bid could boost its chances of getting back to court.
Dr Swire has previously said Megrahi's family could be risking their lives if they raise the prospect of launching a fresh appeal against conviction.
Dr Swire said he wrote to those families whose addresses he still held and asked whether they wished to support the application, with 23 responding positively.
Mr Anwar said: "The number is growing on a daily basis. Each name will be added to the application to the SCCRC."
The solicitor said he expected to meet with the board next month and it would be several months before the body made a decision on whether it will accept the case.
When a convicted person has died, rules allow the High Court to consider an appeal where it considers the person taking the case forward has ''legitimate interest'' in the issue.
In considering whether to accept the new review application, the SCCRC will also have to address whether it is in the interests of justice to do so. The body will also consider the fact that Megrahi abandoned his appeal following a referral from the commission and that neither he nor any member of his family lodged an application for a further review of his conviction prior to his death in May 2012.
The Lockerbie case remains a live investigation, with Scotland's criminal justice authorities making it clear that they will rigorously pursue any new lines of inquiry.
In December, the Libyan attorney general announced he had appointed two prosecutors to work on the case.
They have met Scottish and US investigators who are trying to establish whether there are other individuals in Libya who could be brought to trial for involvement in the attack.
Asked how confident he was that an appeal will ultimately be heard before judges in Edinburgh, Mr Anwar said: "I have confidence that the family members are not going to give up and will continue to fight.
"They will not give up the fight for justice.
"We have confidence in the SCCRC - they did a tremendous job on the last occasion.
"There were six significant grounds of referral back to the appeal court.
"We have a real basis and foundation for this case to be referred back to the appeal court."
Dr Swire said: "Over the years, I still believe that Scottish justice will be delivered and that the justice system has the capacity and the will to see that that is done."
Asked why the families feel they have the required "legitimate interest" for the SCCRC to take on the case, he said: "If you had a daughter aged 23 who was both beautiful and highly intelligent, and she was brutally murdered in a situation where it's clear that the national protection security services had abysmally failed, do you not think that even 25 years later you might want to feel that you had a status in discovering the truth about who murdered her and why she was not protected?
"I think you would find that you would have that need, as I do, and as many relatives still do."