pdflatex cannot handle EPS files directly, and you'll note from the log file that .eps is not among the filetypes it considers:
l.38 ...hics[width=0.75\textwidth]{paperfractalds}
I could not locate the file with any of these extensions:
.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPEG,.JBIG2,.JB2
Therefore, the file has to be converted to a different format, normally PDF. The package epstopdf does this for you, so adding
\usepackage{epstopdf}
to the preamble and compiling with shell-escape enabled (see e.g. How to enable shell-escape in TeXworks?) should take care of that. You may need to use the flag --enable-write18 instead of --shell-escape (they do the same thing, but the former is used by MikTeX).
Note that with newer versions of TeX Live at least, this conversion is handled automatically, so there is no need to add that package or enable shell-escape. I do not know if the same is the case for MikTeX 2.9.
I think LyX perhaps handles these conversions itself, hence not needing that package, but I may be completely wrong. Asking a question at the lyx-users mailing list is probably the best way to figure that out. Also, I though EPS files would work fine when compiling via DVI, so why that doesn't work I don't know.
The log also shows an error from babel, which can occur for example if you compile once, then remove a language option from \documentclass or babel and compile again (see https://tex.stackexchange.com/a/82673/586). \usepackage[english]{babel} should fix that part I guess.
Best Answer
I had the same problem and my solution was: in "Tools -> Preferences -> Converters" consider the "LaTeX (pdflatex) -> PDF (pdflatex)" converter and set
in "Extra flag". If this will not work, delete the converters section in your ./lyx/preferences file (in Linux) and restart LyX.