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The problem was, Boeing hadn't told Lion Air about it, so Lion Air couldn't have told the pilots.
Don't pilots have to retrain to fly a new plane, surely they should have been aware that this is how it works?
Sumo-
the plane’s MCAS anti-stall system weren’t in the Boeing manual
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Pilots do have to get a new type rating to fly a new plane, but the MAX is considered similar enough to previous 737s to not require a new type rating. Not having to train your pilots for a new type approval saves airlines a lot of money, so only one is required for the 737 family and I think it's the same for the Airbus A318/9/20/21.
Pilots do need to do a 'differences course' which is normally delivered online. Ryanair are taking delivery of their first MAX 737s next month (or were meant to be) at Stansted and are/were planning to do the same thing.
The problem here though is that as @fussballclub said the MCAS system wasn't covered in the differences course that the Lion Air pilots would have done. So they didn't even know the system was present, never mind how to disable it.
After the Lion Air crash the Ethiopian pilots would almost certainly have been aware of the MCAS feature and should have been aware of how to disable the system.
fussballclub
Fox
I'm sure it would be more insightful than anything I could offer, but...
Lion Air Flight 610 had problems with it's Angle of Attack (AoA) sensors and the preliminary findings of the investigation were that this problem made the plane's anti-stall system think it was stalling and respond by repeatedly pushing the nose down. It seems the pilots were fighting this system when it crashed.
This system is called a "Maneuvering Characteristics Augmentation System" or (MCAS) and is new on the 737 Max. It's needed because the engines on this model are larger than on previous 737s - because the plane is longer and therefore larger - so they're in a different position: higher and further forward on the wing.
This destabilises the aircraft in pitch at higher angles of attack, so the MCAS system is needed to deal with it. In plainer English, the aircraft is aerodynamically unbalanced, so Boeing created a software fix to deal with it.
The problem was, Boeing hadn't told Lion Air about it, so Lion Air couldn't have told the pilots.
There are many who argue that making planes which can't fly well without needing software to compensate for what could be described as fundamental design issues isn't such a good idea. But if Boeing were going to do that they could at least have made sure this "feature" was well known to anyone flying the plane.
Nobody knows what caused the Ethiopian Airlines crash, but it dived into the ground shortly after takeoff in a manner worryingly similar to the Lion Air crash. So there is unsurprisingly speculation that the MCAS system could have been a factor.