None of the 737s are unstable.

The MAX has the MCAS system which, in rather extreme situations, will apply stabilizer trim input to bias the nose down to avoid a stall. Some other airliners I've flown have a stick-pusher which physically pushes the control yoke forward, quite aggressively, to lower the nose. The 737 does not need anything as aggressive as a stick-pusher to meet the certification requirements.

In the Lion Air crash, judging only by the information that has been released to this point, didn't have an MCAS failure. It had a bad angle-of-attack (AoA) sensor which fed invalid data to the MCAS system.

MCAS will not activate until the flaps are retracted. The flightstat data released on the recent accident indicates that they barely reached 1000'. Depending on the departure profile (NADP1 or NADP2), the flaps are not typically fully retracted until at least 1200' above the airport, sometimes as late as 3300'. Their vertical speed fluctuations started well below an altitude where the flaps would have been retracted. If that data proves correct, it would seem to contradict the theory of another MCAS activation.

The flight recorders have been recovered. If there was some type of aircraft failure, we should start hearing something in the next day or two.