[extrapickles]

From what I can tell, the previous crew did not get lucky, they just followed the checklist which would have solved the issue in this case.

Auto-trim beyond the elevator authority is not a problem as the pilots can take manual control of the trim by grabbing the trim wheel (its in a very obvious spot on the 737).

The actual fix is hard as adding another alarm can get tricky from a UX perspective during an emergency. Probably the only “fix” is to reinforce the value of following the checklist.

[kelnos]

There already is another alarm: an optional "angle-of-attack disagree" indicator that Lion Air was apparently too cheap to install.

Now, that wouldn't have directly pointed to what was wrong, but it would have been pretty suggestive.

(I would suggest, though, that having an optional configuration that lacks robustness for a system that can automatically point the plane toward the ground... a really poor choice of options.)