Here are the steps taken to add the LNCS layout to the local LyX installation:

Download the llncs2e.zip package from Springer’s LNCS author site. Unzip, and copy the folder to the local TeX installation. For Mac, this is at ~/Library/texmf/tex/latex For PC, this is at C:\Documents and Settings\All Users\Application Data\MiKTeX\2.7\tex\latex Update the local TeX installation. […]