The defense team applied to the Superior Court of Justice asking that Lula, who ruled from 2003-2010, remain free despite last week's upholding by an appeal's court of his conviction.
The court sentenced Lula to more than 12 years in prison after confirming the lower court conviction for corruption and money laundering. Lula, a left-wing firebrand who leads in opinion polls ahead of October presidential elections, claims to be the victim of a political persecution.
The latest court ruling could see him sent to start a prison sentence within months, although he still has a last few narrow options, including Tuesday's filing at the justice court and at the federal Supreme Court.
Lawyers also filed papers with the United Nations human rights body in Geneva accusing the court case against Lula of violating his rights to a fair trial.