The flight took off from Jakarta around 6.20am (10.20am AEDT) and was due to have landed in Pangkal Pinang, capital of the Bangka-Belitung tin mining region, an hour later, the Flightradar 24 website showed. As per a report by Straitstimes, the contact was lost around 6:33 am. It is unclear if there are survivors.
Citing the VP of a leading airline in India that operates the Boeing 737, the daily reported that Suneja was considering returning to India.
The search and rescue agency said the flight ended in waters off West Java that are 30 to 35 metres deep.
Fuel and debris have been found at the suspected crash site, and divers are being brought in to access the wreckage.
At an earlier news conference, officials said the plane had been carrying 178 adults, one infant and two babies, as well as two pilots and five cabin crew.
Lion Air has confirmed the flight was commanded by Captain.
Three of those on board were trainee flight attendants and one was a technician.
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A plane with more than 180 people on board has crashed off the coast of Indonesia. They routinely took this flight.
"We can confirm that one of our flights has lost contact, its position cannot be ascertained yet", Lion Air spokesperson Danang Mandala Prihantoro said.
Delhi's Bhavye Suneja was working with Lion Air for the past 7 years.
"At the moment personnel from Karawang water police unit are heading to the coordinates to check whether the information we received was accurate", Waluyo told broadcaster Kompas TV.
Lion Air is the largest privately-owned Indonesian airline and among the major customers for Boeing and Airbus in Asia.
The pilots had asked to turn back to airport shortly before losing contact with air traffic control, the report said, quoting spokesman for Indonesia's air navigation authorities.
"We are also confused about the why, since it was a new plane", he told Reuters.
Indonesia relies heavily on air transport to connect its thousands of islands but has a poor aviation safety record and has suffered several fatal crashes in recent years.
The Lion Air jet that crashed was fit for operations, the airline said in a statement.