A termsheet reviewed by Reuters said the proceeds of any deal would go towards longer-term leases more akin to owning planes, as well as towards its general operations. Lion Air has one of the industry's biggest outstanding orders with both Boeing and Airbus.
The float plans come as the Indonesian market is stabilising after years of overcapacity.
"There has been a dramatic change in the Indonesian market as all airlines reduced capacity and that resulted in significant increases in yields and therefore the market became profitable," said Brendan Sobie, an independent aviation analyst based in Singapore.
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The IPO also comes more than a year after the October 2018 fatal crash of a Lion Air Boeing jet that killed all 189 people on board.
The accident, followed within five months by another at Ethiopian Airlines, led to the global grounding of all Boeing 737 Max planes and triggered a crisis for the U.S. planemaker.
Last October an Indonesian accident report into the disaster focused on flaws in Boeing cockpit software, while also recommending better training at Lion Air and improved U.S. and local regulation.