Something really has gone wrong with this flight soon after take off.
Data from
https://www.flightradar24.com/blog/flightradar24-data-regarding-lion-air-flight-jt610/Graph of entire flight altitude/rate of climb
Graph of takeoff altitude/rate of climb
Flight is not a smooth climb to flight level, altitude and rate of climb are all over the place.
Indicates flight being flown manually.
Graph of last minute of flight altitude/rate of climb
This is at what appears on radar maps (and radio comms) to be at the point where the plane was to turn around to return to the airport.
-33,000 ft/minute, no chance of survival.
I think the altitude values don't show the true horror of what occurred
My guess is the plane in fact attempted the turn while descending rapidly, this caused it to roll over and become impossible to recover from.
Various theories about causes, we can rule out engine problems, as planes with no working engines can still fly to some extent.
That just leaves:
A) pilot actions (combined with faulty instrumentation).
B) flight control malfunction or mechanical failure.
A is looking very likely, but B could also be involved or the main cause.
The crash people should be looking at is Air France Flight 447, where inconsistencies between the airspeed measurements were involved.