Lula's defense team hopes to overturn a decision by Sergio Moro, a federal judge and head of a key corruption investigation, that determined Lula had to begin serving a 12-year sentence for accepting bribes.
Lula was imprisoned on April 7, effectively derailing his bid to run for a third term in October elections.
STF judges will have until midnight of May 10 to submit their electronic votes, without having to meet in person to debate the case.
Should all the votes be in before the deadline, the much-anticipated results could be announced earlier.
Lula's Workers' Party (PT) has said he remains their candidate despite his legal troubles, which it claims have been politically motivated to keep him out of the race.
His lawyers argue that Moro's decision to have him begin his sentence was premature, since they have not exhausted his appeals process.
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