Respecting what follows, your corrections of my misunderstandings
are solicited.

OK.  The digest goes like this:

1. It is the case that all installs to my single user computer are for
use by all users.

2. MiKTeX has a requirement that the user maintain any *custom*
class, style, include, other tex files, and layout files.  One may
choose to use any of the directories listed in MiKTeX Settings,
though it would generally be better practice to add a new path
to the available roots, and store files in that root, thus obtaining
an expected retention of setting in the face of MiKTeX upgrade.
Of course, if the settings are lost, then the path will need to be
added to any upgrade.

The *user config* directory is indeed not yet made, as in mkdir.
I also note that the *user config* *user data* and *common*
roots may not be altered, at least via MiKTeX Settings.

3. To be sure, when I mentioned following the given advice, I did
follow all parts.  Particularly, I refer to the notions of reconfiguration
for both LyX and MiKTeX.  Thus, when I added paths for the
missing texmf subtree, I not only added a root and subtree to
MiKTeX, the FNDB was refreshed and Update Formats (thought
this latter step may have no direct impact upon my current need)
need), and also reconfigure and restart LyX.  Both of these tasks
have been performed multiple times, and these times being
subsequent to alteration of roots and addition of files thereto.

4. I did alter the layout file to read

\DeclareLaTeXClass[llncs]{article (Springer LNCS)}

Upon thereafter reconfiguring LyX, the class was recognised.
So, now I am moving along.

I had previously altered this statement, to include [springer]
and not [llncs], owing to some suggestion hinted by other
layout files.  The correction to the bracketed label brought
access to the document class llncs.

Thanks to all for all the help you have given.  Perhaps some
of this information will find its way into the LyX documentation.

wrb



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