The lawsuit accuses the US aircraft manufacturer of failing to inform pilots and airlines of a feature with its new 737 Max plane system that could “push the nose down unexpectedly”.
Investigators have been looking into reported technical issues.
Boeing maintains that it is “confident in the safety of the 737 Max”.
Lion Air flight JT 610 was carrying 189 people when it crashed on 29 October.
It plummeted into the Java Sea following a request from the pilot for permission to turn back to the airport just moments after taking off from Jakarta.
It was later established that the aircraft had had an airspeed indicator problem on its final four flights.
What does the lawsuit say?
A complaint was filed by a Florida-based law firm on behalf of the parents of Rio Nanda Pratama, who was on board the ill-fated flight JT 610.
The lawsuit focuses on the 737 Max’s new automated flight control system, which it says was designed to help prevent pilots from raising the aircraft’s nose “dangerously high”.
However, the lawsuit adds: “Under certain conditions [the system] can push the nose down unexpectedly and so strongly that the pilot cannot pull it back up in time to avoid a crash.
“This automated feature can be triggered even if pilots are manually flying the aircraft and don’t expect flight-control computers to kick in.
“It is particularly surprising to hear from safety experts and the heads of pilots’ unions that Boeing failed to warn its customers and the pilots of its new 737 Max aircraft about this significant change in the flight-control systems.”
Boeing, meanwhile, has said that it is not able to “discuss specifics of an ongoing investigation”.
Mr Pratama was a passenger on flight JT 610 travelling home to marry his fiancée, Intan Syari.
Ms Syari, who said she wanted to fulfil his last wish, appeared alone wearing her white gown and wedding ring in photos posted to her Instagram account earlier this week.
What went wrong with the flight?
There is as yet no indication of what caused the crash but the plane had experienced technical problems related to airspeed and altitude readings.
Indonesia’s National Transportation Safety Committee said an “angle-of-attack” sensor had been changed the day before the crash.
One of the black box recorders from the flight has been retrieved but authorities say it could take months to analyse the data from it.
The plane was making a one-hour journey to the western city of Pangkal Pinang when it went down. No survivors were found.