Depression is a common enough illness, and can be generally managed well. Like any other illness it does depend on the patient wanting to get well, and cooperating, despite the understandable effect of mental illness. Lubitz still had responsibility for himself. He chose to disregard this. Now suicide tends to be a complex thing and many at the point of suicide tend to think logically but in ways which do not take into account any consequence after the act itself. Think of the many people who have chosen "death by cop" - Its planned and logical, however horrific the consequences.
However, it remains Lubitz own responsibility to state that he is not well and request that he is taken out of service for a while. It is not entirely the doctor's fault in failure to report, even if it were legal. Lubitz may well have been evasive in his responses to the doctors, who may have suspected things may be badly wrong but do not know or could not imagine what he would do.
I feel that the scenario with the healthcare professionals would be something like - Are you feeling suicidal? Yes. Have you any plans? No. Now what do you do about that? Even though the body language may be telling you that the patient is lying, what do you do?
Equally interesting is that Lubitz was prescribed antidepressants only 8 days before his suicide. For someone with a long term health condition that is quite recent. If it was the first time he was prescribed antidepressants (which I doubt) then it would certainly have been irresponsible to have gone to work. If it was a change of antidepressants, it would be interesting to know which one, as some of them in the first few days can amplify suicidal feelings. In any case, 8 days after taking an antidepressant, it would have been unwise to fly an aircraft and I am sure that the prescriber would have said so.