Citing documents found by Germany's air transport authority, the Bild am Sonntag said the doctors wrote that "Lubitz should continue to receive psychological treatment, even though he was deemed fit to fly" by an independent expert in 2009.
Lubitz had interrupted his flight training in 2009 and had told Lufthansa about his illness.
The report does not specify if Lubitz had indeed benefited from continued treatment.
A Lufthansa spokesman declined to comment when contacted by Bild.
French investigators believe that Lubitz deliberately slammed the plane operated by Lufthansa subsidiary Germanwings into the French Alps on March 24, killing all 150 people on board.
Germany's air transport authority said it never had access to Lubitz's medical files, and was only able to examine them three days after the crash.
German prosecutors have said Lubitz was diagnosed as suicidal "several years ago", before he became a pilot, but had appeared more stable of late.
Doctors had recently found no sign that he intended to hurt himself or others, but he was receiving treatment from neurologists and psychiatrists who had signed him off sick from work a number of times, including on the day of the crash.
Police found torn-up sick notes during a search of his apartment after the crash.