Sort of the wrong question, albeit same outcome. It should be "can such a person get a Class 1 Medical?".
That said, I do not know the answer...
Since April 2013 AMC1.MED.B.055 Psychiatry, AMC1.MED.B.060 Psychology and AMC1.MED.B065 Neurology would apply.
I honestly do not know how it is handled at lufthansa, they do have several AeroMedical Centers that can on their own issue special approvals. However, as far as i know the company only gets to pay the bill and a fit/unfit message plus a copy of the medical, nothing else. Again, even if it is a company AME doctor/patient confidentiality does apply, except for those data that have to be submitted to the authority, however not to the company.