LaTeX.org

Description here (LyX wiki) may help. It is mentioned that there are bugs in MikTeX and usage of TexLive is recommended.

I think simply installing ImageMagick solves (the default image file -> pdf converter). After installation, you need to do Tools -> Reconfigure from the LyX menu).

I guess behind the dialog you can see a part of LyX text is selected in blue, and that part is the place LaTeX error has occurred. Since LaTeX error is not always visible in LyX, the selected text may look irrelevant but error occurs around there.

I think reinstallation will do it, doesn't it?

I guess this prompt from MikTeX pops up because the user tried to open/create a LyX document whose language is set to Japanese. Unfortunately, MikTeX doesn't include pLaTeX (a Japanese LaTeX), you need to set document language to other languages (via Document > Settings > Language) or to use LaTeX ...