Libyan Abdelbaset al-Megrahi is the only person to have been found guilty of the bombing of Pan Am flight 103 over Scotland in which 270 people were killed.
Megrahi, who was released from jail by the Scottish Government on compassionate grounds after being diagnosed with prostate cancer, died in 2012 protesting his innocence.
British relatives of the victims are now poised to apply to the Scottish Criminal Cases Review Commission (SCCRC) in the hope of having the conviction overturned, according to Dr Jim Swire, whose 23-year-old daughter Flora died in the bombing in December 1988.
He made the announcement at a screening of a new documentary that claims the bombing was ordered by Iran - in retaliation for a US strike on an Iranian passenger plane - and not Libya.
The evidence presented in the Al Jazeera film has been dismissed by the Crown Office as "nothing new".
But Dr Swire said it "matches very closely" the information that some relatives had gathered in the 25 years since the atrocity.
He said: "Some British relatives have decided that enough is enough and we will be applying within weeks for a further appeal against the Megrahi verdict.
"We as relatives have a right to know who killed our families and why the British Government and authorities responsible for the safety of the aircraft failed in their duty. Until we get the answer to those questions, we are not going away."
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, potentially leaving it to victims' families.
If successful, a new application to the SCCRC could start the third appeal into the conviction.
Dr Swire said he was "confident" that the SCCRC would find in favour of the application. The families hope that overturning Megrahi's conviction could pave the way for an inquiry.
He said it was "extremely encouraging" that the documentary, to be broadcast tonight on Al Jazeera English, had come to many of the same conclusions.
It includes an interview with former Iranian intelligence officer Abolghassem Mesbahi, who claims that the bombing was ordered by Tehran and was carried out by the Syrian-based Popular Front for the Liberation of Palestine-General Command (PFLP-GC) in retaliation for a US navy strike on an Iranian commercial jet six months earlier, in which 290 people died.
The US ship apparently mistook the plane for an F-14 fighter jet.
Mr Mesbahi tells the programme: "Iran decided to retaliate as soon as possible. The decision was made by the whole system in Iran and confirmed by Ayatollah Khomeini.
"The target of the Iranian decision makers was to copy exactly what's happened to the Iranian Airbus. Everything exactly same, minimum 290 people dead. This was the target of the Iranian decision makers."
US Defence Intelligence Agency cables at the time reported that the leader of the PFLP-GC had been paid to plan the bombing, the film claims.
It also includes an interview with former CIA agent Robert Baer, who was involved in the Lockerbie investigation.
He said: "Six days after taking down the Airbus there was a meeting in Beirut, we know where it occurred.
"The Iranians went to the PFLP-GC, the break-off faction, and said, 'alright you guys know how to bring down airplanes, bring down five, five, civilian airliners'."
A Crown Office spokesman said: "Mesbahi's claim that Iran was responsible was first reported in the media in the late 1990s and was available to the defence before the trial but they did not call him as a witness.
"The wider alleged involvement of the PFLP-GC has been repeatedly reported over many years but was addressed in full and rejected at the original trial.
"The only appropriate forum for the determination of guilt or innocence is the criminal court and Mr Megrahi was convicted unanimously by three senior judges.
"His conviction was upheld unanimously by five judges, in an Appeal Court presided over by the Lord Justice General, Scotland's most senior judge.
"As the investigation remains live, it would not be appropriate to offer further comment."
Megrahi lost his first appeal in 2002, one year after he was found guilty of mass murder and jailed for life.
The SCCRC recommended in 2007 that Megrahi should be granted a second appeal against his conviction.
He dropped his appeal two days before being released from prison in August 2009 on compassionate grounds.
In December, the Libyan attorney general announced he had appointed two prosecutors to work on the case.
For the first time they 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.