Hello,
Older versions of Lightning had a defect that caused Lightning to request a password when viewing certain PDF files, even if the file is not password-protected. Unfortunately, there is no way around this problem.
In the most recent version of Lightning, the PDF viewing capability has been removed, as we believe that users will get greater benefit from an external PDF viewer.
I would strongly recommend you install an alternate PDF viewer, such as Foxit Reader or Sumatra PDF (if you prefer lightweight viewers) or Adobe Reader (if you prefer having a more feature-rich viewer).
Sorry I couldn't be more help,