The nearly new Boeing 737 MAX 8 went down in the Java Sea shortly after taking off from Jakarta's Soekarno-Hatta International Airport on Monday morning with 189 passengers and crew on board.
The devices record information about the speed, altitude and direction of the plane as well as flight crew conversations and could hold vital clues to the cause of the deadly accident.
Spokesman for Indonesia's search and rescue agency Yusuf Latif confirmed the finding of an "orange object", but did not confirm it was the black box.
The plane had showed signs of technical problems the day before the catastrophic crash during a flight from Bali.
Lion Air Managing Director Daniel Putut said the airline had "many questions" for the Chicago-based company and they would discuss the delivery of remaining aircraft 737-MAX models, Indonesian news website tirto.id reported.
In April, the airline announced a firm order to buy 50 Boeing 737 MAX 10 jets, with a list price of $6.24 billion.
It shows passengers' boarding passes being checked and people walking along a concourse and then down stairs with bright red and white Lion Air jets visible on the tarmac.
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Indonesia may review the lower limit of its airfares and consider increasing the rates set by low-cost carriers, the transport minister said on Thursday.
A navy diver on board a search vessel told the broadcaster Metro TV that his team found the orange cylinder containing the recorder among debris on the muddy sea floor.
Lion Air only regained access to the European Union in 2016.
The doomed plane, which went into service just a few months ago, was en route to Pangkal Pinang city when it crashed into the Java Sea off Indonesia's northern coast moments after it had asked to return to Jakarta on Monday.
The crash has also resurrected concerns about Indonesia's patchy air safety record which led to a now-lifted ban on its planes entering USA and European airspace.
A team of rescuers heard pings from an underwater locator beacon with a distinct sound and interval between them, making it very likely that the wreckage and the location of the flight recorder have been identified, authorities said.
Haryo Satmiko, Deputy Director of the National Transport Safety Committee, told CNN that while the pings had been detected, investigators needed more "technical efforts" to find the exact location of the black boxes.
Dozens of relatives of the missing gathered at a police hospital in East Jakarta, where body bags had been brought for forensic experts to try and identify victims, with techniques such as taking swabs of saliva from families for DNA tests.
Its airlines were banned from flying to the United States in 2007 because they were "deficient in one or more areas, such as technical expertise, trained personnel, record-keeping, or inspection procedures", the Federal Aviation Administration said.