I found the problem,
A little clarification for those who want to install a class in LyX. Please follow these steps that are mentioned in the previous link:
llncs2e.zip, which contains
llncsdoc.sty. I just googled for a download link and got mine from here.
Copy those files to the folder
...\MiKTeX 2.7\tex\latex\lncs, where
...\MiKTeX 2.7 is the folder in which MiKTeX is installed. On some systems, copy to
... \MiKTeX 2.7\texmf\latex\lncs. The
lncs folder will probably need to be created.
Mine was in
C:\Program Files (x86)\MiKTeX 2.9\tex\latex, where I had to create the
lncs folder (which requires admin privilege escalation). I extracted
llncsdoc.sty to this folder.
from the command line.
Run MiKTeX Settings. Press "Refresh FNDB" under General. Then, possibly, "Update Formats".
Open LyX and select Tools -> Reconfigure
But be sure to put the
llncsdoc.style files in:
PS. Create the folder
lncs if it doesn't exist.