Lawyer Aamer Anwar joined family members and supporters to hand files to the Scottish Criminal Cases Review Commission (SCCRC) in Glasgow.
Megrahi was convicted in 2001 of the 1988 atrocity which killed 270 people. He was jailed for 27 years but died of prostate cancer aged 60 in 2012 after being released on compassionate grounds in 2009.
He lost an appeal against his conviction in 2002, with the SCCRC recommending in 2007 that he should be granted a second appeal.
He dropped the second attempt to overturn his conviction in 2009, ahead of his return to Libya, but his widow Aisha and son Ali met Mr Anwar late last year to discuss a posthumous appeal to overturn the murder conviction.
The SCCRC will now decide whether there are grounds to refer the case to the appeal court.
The move has the support of Jim Swire, who lost his daughter Flora in the bombing of Pan Am Flight 103, and Rev John Mosey, whose daughter Helga also died.
It is believed the new appeal bid is based on concerns over the evidence that convicted the Libyan, including that given by Maltese shopkeeper Tony Gauci, who died last year.
Mr Anwar said: “It has been a long journey in the pursuit for truth and justice. When Pan Am Flight 103 exploded over Lockerbie on 21 December 1988, killing 271 people from 21 countries, it still remains the worst terrorist atrocity ever committed in the UK - 28 years later the truth remains elusive.
“The reputation of Scottish law has suffered both at home and internationally because of widespread doubts about the conviction of Mr al-Megrahi.
“It is in the interests of justice and restoring confidence in our criminal justice system that these doubts can be addressed. However the only place to determine whether a miscarriage of justice did occur is in the appeal court, where the evidence can be subjected to rigorous scrutiny.”