Witness after witness (passengers and ground-based) report the plane "dropped" into the water BEFORE reaching the runway. I.E. - NOT an overrun.
One eyewitness perhaps can be discounted as unreliable or suspect - but when there are multiple witnesses reporting the same thing, it starts to carry a lot of weight. Certainly more weight than the imaginings of a non-witness at a keyboard 1,000s of miles away.
Rumored MAYDAY tends to indicate a loss of thrust without sufficient altitude/energy to make the runway. Think BA38, minus the smooth grass threshold. For doubly good reasons, the captain (along with everyone else) survived, and will be able to tell his tale.
As to WHY there may have been a loss of thrust - bird strike, fuel exhaustion, fuel starvation, internal mx problem,
TBD. Likely not fuel ice in the filters, in the tropics in April (but you never know until you check!)
Direction the airplane is pointing after the crash is certainly relevant - but not necessarily a perfect indicator of direction of flight. (and in the pictures, is not aligned with EITHER runway 27 or 09).
If the Hudson had been 6 feet deep and full of coral knobs, Sully might well have ended up pointing back the direction he came, also.
Lion Air's reputation? Maybe a factor, maybe not. "Even a paranoid can have real enemies" - and even a "bad" airline (or a "bad" pilot) can have an accident that isn't its/his/her fault.