If Indonesia's Supreme Court approves the appeals, the defendants will seek a retrial in hopes the proceedings would be fairer, their lawyer, Mohammed Mahendradata, said on Friday.
The three - Imam Samudra, Ali Gufron and Amrozi Nurhasyim - are among 30 people convicted over the Bali nightclub blasts that killed 202 people, many of them young Australian tourists.
They are alleged members of the al-Qaeda-linked Jemaah Islamiyah armed group, blamed for a string of attacks in Indonesia, including another spate of bombings in October 2005, also on Bali, that killed 20 people.
The three are scheduled to be executed on August 22.
Mahendradata noted that Indonesia's constitutional court ruled in July 2004 that new laws passed after the 2002 bombings could not be used retroactively.
"The criminal code stipulates that if there is any change in the law then the law applied should be beneficial to the defendant," Mahendradata told reporters in the capital, Jakarta.
He said the appeal will also convey to judges a request from Umi Badriha, the mother of lead defendant Samudra, to be executed along with her child.
It is highly unlikely such a request will ever be granted.
In the past, the three defendants have said they wanted to die and become martyrs for their cause.
Separately, the lawyer said that he would sue the Indonesian attorney-general's office if the executions are carried out before appeals are exhausted.
"The executions cannot be done because they should wait for the judicial review process," he said.
Under Indonesian law, a convict may still challenge a verdict upheld by the Supreme Court through another appeal called a judicial review which requires strong new evidence.
Executions in Indonesia are normally carried out by a firing squad.
Support for bombings
Meanwhile, a new poll showed that one in five Indonesians believed the 2002 Bali bombings were justified because of the decadent lifestyle there.
The survey of 1,200 people, carried out by Jakarta's State Islamic University, also found that 16.1% of respondents supported the September 11 attacks on the United States that killed almost 3,000 people.
Jajat Burhanudin, author of the study, blamed the findings on Islamic teachings that he said justified violence in the name of the faith.
"The behaviour of religious violence that is developing in Indonesia at the moment is strongly rooted to the understanding over Islamic teachings that justify violence," he said.
"There must be a firm and strategic policy from the government to stop violent acts in the name of religion that have been growing in Indonesia lately," he said.
About 85% of Indonesia's 220 million people are Muslim, making it the world's most populous Islamic country.
Many mainstream Muslims around the world have condemned militant violence, such as the Bali bombings and September 11, as not in keeping with the teachings of their religion.