Indonesian accident investigators said an airspeed indicator of a Boeing Co 737 MAX plane that crashed last week was damaged for its last four flights, but United States authorities responded cautiously to suggestions of fleet-wide checks.
Southwest had 23 737 Max 8 in its fleet as of September 30, with nine more to be delivered by the end of the year.
The company noted that the warning provides guidance to pilots and operators of new aircraft on how to proceed in these circumstances.
Boeing is preparing a bulletin to all operators of the new 737 model warning that "erroneous readings" from a flight-monitoring system can cause the planes to aggressively dive, Bloomberg quotes an anonymous source as saying.
Moments earlier, the pilots radioed a request to return to Jakarta, but never turned back toward the airport, according to Indonesia's safety commission and flight-tracking data.
On a previous flight from Bali to Jakarta, the same jet's angle-of-attack sensor feeding the captain's displays registered a 20-degree difference from the device on the copilot's side of the cockpit, the committee said.
Distraught families begged the founder of Lion Air to tell them why the plane, which was found to have technical problems, had been passed fit to fly.
Indonesia's search and rescue agency said they are still working to locate the cockpit voice recorder which they believe is amongst the other wreckage under the sea.
False readings from the sensor can cause the aircraft to pitch downward in an attempt to avoid a stall when the plane is not being flown on autopilot.
Boeing warned airlines about the features of the aircraft.
The transport ministry said it would launch an immediate investigation. They were flown to the capital later Wednesday evening aboard a different aircraft.
After an engine on a Southwest Airlines Co. plane fractured earlier this year over Pennsylvania, killing a passenger, CFM International Inc. issued multiple bulletins to operators of its CFM56-7B power plants.
In addition, aviation regulators such as the U.S. Federal Aviation Administration and the European Aviation Safety Agency often follow such actions by mandating that carriers follow the bulletins.
The directive addresses a potential problem where incorrect angle of attack sensor input can cause the flight control system to send commands to the horizontal stabiliser to push the nose down.
Such an issue arose in 2016 at Rostov-on-Don Airport in Russia when a FlyDubai 737-800 nosed over and slammed into the runway at a steep angle, according to an interim report by Russian investigators.