I find it troubling that so many self-professed "professionals" on here are tiptoeing around the F/O's documented history of mental illness and a system that allows such a person with that history person to hold a medical certificate of a class sufficient for a commercial pilot certificate to remain valid. Sorry (not) if that sounds "discriminatory" but in aviation, particularly for those involved in commercial/common carriage of passengers with no say who occupies the front seats, our whole careers are discriminatory in terms of performance and health standards that must be met.
Depression is a mental illness. This should have put a big question mark over his suitability to fly a commercial or any other type of aeroplane. It would seem to me that Lufthansa/German Wings are culpable. They knew he had been ill and yet allowed him to take charge of a Commercial Aircraft and the lives of 150 people
The reason people "tip-toe" round it is we (those of us who are pilots) know very little about it.
The question of whether he was fit to fly or not is purely in the hands of the regulatory medical authorities: EASA / LBA. It is
not to do with the airline, unless in that airline there is some overlap between employer and medicals.
For most airlines, as I said earlier, you either hold a medical certificate or not. You tell the employer the expiry date - they might even want to check the certificate. End of.
At the large airline I work for, I can choose to use their medical department or not for my medicals. There are "Chinese walls" between them as medical examiners and the employer... but not really relevant anyway, since I, and likely the majority, do medicals with independent AMEs.