JAKARTA, Indonesia — The government safety inspector had spent all night at the Makassar airport, in eastern Indonesia, several years ago, poring over a Lion Air jet that had suffered a hydraulic failure. Telling airline employees that the plane was to be grounded until the problem was fixed, the inspector went back to a hotel for a quick shower.

When the inspector returned, the plane was on the runway, about to take off.

Furious, the inspector demanded that the passengers disembark. But a supervisor with Lion Air explained how the airline had gone over the inspector’s head: National government officials in Jakarta, the Indonesian capital, had given permission for takeoff, the inspector said. The plane was in the air minutes later.

The notorious safety record of Lion Air, Indonesia’s largest carrier and one of the world’s fastest-growing airlines, is back in the spotlight after the crash of Flight 610, which hurtled nose-first into Indonesian waters with 189 people on board just minutes after takeoff on Oct. 29.

Investigators are trying to figure out what deadly alchemy of factors caused a new Boeing jet to plunge into the water at more than 400 miles per hour.