Family lawyer Aamer Anwar said that a dossier of evidence will be delivered to the Scottish Criminal Cases Review Commission, which will review it and decide whether to hand the case on to an appeals court.
"I wish to pursue this appeal in my husband's name to have his conviction overturned, to clear his name and to clear the name of my family," al-Megrahi's widow Aisha told the Daily Mail.
"The world will say sorry to my husband and my family one day."
Al-Megrahi was convicted of bombing Pan Am Flight 103, a New York-bound Boeing 747, in December 1988. The plane exploded over the Scottish town of Lockerbie, killing all 259 people on the plane and another 11 on the ground.
Al-Megrahi was head of security of Libyan Arab Airlines and was accused of masterminding the bombing. His trial began in 2000, and in 2001 he was found guilty by a Scottish panel of judges and sentenced to life in prison.
Despite repeated attempts to appeal, al-Megrahi never found purchase. However, he was released from prison on compassionate grounds in 2009, as he had been diagnosed with terminal prostate cancer. He died in 2012, maintaining his innocence throughout.
"We must not forget that Megrahi was found guilty of this atrocity," said Douglas Ross, a spokesman for Scottish Tory justice. "While an appeal must be given due process, to suggest that the world owes him and his family an apology will be galling for many of the friends and relatives of those who lost their lives in the Lockerbie disaster."
Some of the victims' families have backed the past appeal attempts, including Doctor Jim Swire, whose daughter Flora was aboard Pan Am 103.
Most of the families maintain al-Megrahi's guilt, however. Peter Lowenstein, the father of the then-21-year-old Alex who also died in the bombing, slammed the court's consideration. "Over the years there's been no evidence showing Megrahi was not guilty. He was found guilty by a Scottish court and, as far as I'm concerned, he murdered 270. I don't think his family should have the right to try to show he was innocent. The whole thing is an outrage."
Susan Cohen, who lost her daughter Theodora in the attack, said: "The people who insist on Megrahi's innocence are using alternative facts, they're conspiracy theorists. In terms of the appeal, a lot of the people involved are dead and probably by the time this is concluded some of the victims' relatives will also be dead."
