Based on an informal discussion entitled "how to update .aux file in LyX?" (with the current "stable branch maintainer", Jürgen Spitzmüller) it seems that LyX automatically reruns a file based on an evaluation of the .log file. Another motivation for this stems from the LyX documentation on Customizations (under the menu item Help > Customizations, section 5 Installing New Document Classes, Layouts, and Templates):
First, let us a say a few words about how one ought to think about the
relation between LyX and LaTeX. The thing to understand is that, in a
certain sense, LyX doesn't know anything about LaTeX. Indeed, from
LyX's point of view, LaTeX is just one of several “backend formats” in
which it is capable of producing output. Other such formats are
DocBook, plaintext, and XHTML. LaTeX is, of course, a particularly
important format, but very little of the information LyX has about
LaTeX is actually contained in the program itself.
For example, the default LaTeX warning message
LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
would initiate a re-compile, while the etaremune-specific warning message
LaTeX Warning: Etaremune labels have changed.
Rerun to get them right.
was "a specific syntax" that needed to be considered. Another example from the totcount package:
Package totcount Warning: Rerun to get correct total counts on input line ???.
that is not referenced as a "LaTeX warning", but rather a "package warning". Moreover, there seems to be no interest in implementing a forced, full, recompile (more than once) option in LyX. So, if the change does not initiate "a known warning", no recompile will be performed.
A suggestion would be to post this, in the form of a full example of your document usage/structure that shows the validity of such an option as being a feature, on the LyX mailing list. See their Get involved or Mailing Lists page for a reference.
The problem was due to one of citations, in which I've used "Text before" parameter and inserted a n-dash in it. LyX put it in the code as \citet[pp. 5–10]{author2000title} and that prevented LyX even from launching verification procedure, i.e., it couldn't report that was the mistake.
Sorry for bothering you.
Best Answer
OK. I dug a little more through the Lyx's menus and I found the answer.
The solution is to go the menu: Document-> Change Tracking -> Show changes in Output.
Also, worth to be mentioned is that it appears that this works for all 3 PDF export methods including pdflatex.
I am wondering then if this wiki document is wrong or obsolete?