Let's take it to the extreme - supposing the industry decided to subject every pilot to a mental health examination (carried out by a mental health professional) to determine whether the pilot was mentally fit for duty.
I suspect even Lubitz would have passed this assessment on this day. He would have made sure of it - this was going to be a big day for him.
There was an infamous rape/murder in Melbourne a short while ago in which the perpetrator had been jailed previously for similar offences but released early on parole based on the fact that he had persuaded officials (which would have included mental health professionals) of his complete reform. Only months later, he raped and murdered another young lady. Google Jill Meagher.
The point is, real psychopaths are good at hiding it.
Fortunately, not many of them become pilots. The statistics are on our side.