Much good information has come from Bob Lounsbury.  Thank you
for the attention to detail.  Where would I have been expected to
read of the requirement to create such a texmf sub-directory, given
that it was not created automatically by either MiKTeX or LyX?  Indeed,
why was such a directory not so automatically created, when it is
apparently of some need to the system that these directories exist?

I did follow the given advice, and created a *texmf* directory, then
added the .\tex\latex  and .\tex\bibtex\ ....   sub-directories.

These acts were followed by adding a root path to MiKTeX2.7
settings, and reconfiguring the file name database.  Actually, we
have performed this act about five times.  I have even changed the
search order for these roots, and then updated the database.  So,
the layout file shows up in the TeX Information but, in the Document
Settings, the document class Springer LNCS shows up as unavailable.

Thus, may we return to a previous question?

I did find adjacent to the <user config> directory a 
reference to LyX15, and in that directory one may
find a file called textclass.lst, within which one
finds the following lines:

 >  "article" "article" "article" "true"
 >
 >  "llncs" "springer" "article (Springer LNCS)" "false"
 

Why should this file textclass.lst be so constructed?

Other ideas are of course solicited.

It might be of interest that some hacking did produce some positive
results, though not quite what I need.  Basically, I put the class and
style files in the same directory as my .lyx file, and modified the
\textclass to be llncs.  Under this condition, I could generate a PDF.

wrb




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