The 2-month-old Boeing plane plunged into the Java Sea on Monday just minutes after takeoff from Jakarta, killing all 189 people on board.
Locating the fuselage will bring the search effort closer to finding the plane's flight recorders, which are crucial to the accident investigation.
The company said its dismissal of Muhammad Asif had come on the orders of the transport ministry.
The aircraft, a brand new Boeing 737 Max, was flying erratically on Monday morning as well.
Lion Air boss Daniel Putut said the U.S. company needed to be asked: 'What's the matter with this new plane?'
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Indonesia has ordered the inspection of all Boeing 737-MAX 8 aircraft following Monday's Lion Air crash.
Lion Air has ordered 50 of the MAX 8 planes and one of its subsidiary airlines was the first to operate the new generation jet past year.
An Indonesia safety official said among the issues was unreliable airspeed readings.
"We dug and we got the black box", a diver, identified as Hendra, told broadcaster Metro TV on board a search vessel, the Baruna Jaya, describing how his team found the orange-coloured box intact in debris on the muddy sea floor.
There is as yet no indication of what caused the crash, though there are reports the aircraft had experienced technical problems on earlier flights.
"The Lion plane requested to return back to Bali five minutes after take-off, but then the pilot said the problem had been resolved and he was going to go ahead to Jakarta".
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They agreed to work together to find Mann and his son, believing that Mann had entered the US illegally after taking the baby. Mann was living in Vernon, Conn. with his son who was born as Jermaine Mann but was unknowingly using a fake name in the U.S.
Indonesian rescuers said that the Boeing crash there were no survivors.
The development comes as Boeing officials are to meet with Lion Air on Wednesday, after Indonesia ordered an inspection of the U.S. plane maker's 737-MAX jets.
National Transportation Safety Committee investigator Ony Soeryo Wibowo addressed media in Jakarta following the discovery, explaining that the particular piece of equipment was not recovered in its entirety.
The disaster has reignited concerns about safety in Indonesia's fast-growing aviation industry, which was recently removed from European Union and USA blacklists. A remote-operated vehicle was sent to the black box location "but the currents on the seabed were very strong, the ROV was carried away", Mr Syaugi said.
Search teams have taken up the grim task of separating human remains from plane debris and recovered personal effects, sending the body parts - including from an infant - to hospital for DNA testing.
At one point, the passenger who shot the video, Paul Ferdinand Ayorbaba, zooms in on the flight number on his boarding pass.
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The country has had issues of safety and poor management in the past and its airlines were banned from flying into European airspace until 2016.