This article goes into what the pilots of the Lion Air 737 Max 8 (and presumably the Ethiopian Airlines one as well) would have had to do in order to regain control over the aircraft. We’re starting to get hints of the task saturation and alert overload both sets of pilots may have faced as they tried to handle the situation:

The Lion Air crew would have had to accomplish this while dealing with a host of alerts, including differences in other sensor data between the pilot and co-pilot positions that made it unclear what the aircraft’s altitude was.

Thanks to Courtney Eckhardt for this one.