The convert command does work ok. I went ahead and tried
convert filename.eps filename.pdf
The PDF is a bit grainy and unresolved, but there is definitely an image there,
whereas in the document it's an empty bounding box.
I also tried opening filename.eps in Adobe Illustrator and it complained about
the following fonts
CMMI7:
Default font substituted for missing font.
and the same message for CMR7, CMSY7, CMMI10.
My colleagues is running Lyx 1.5.xx, with MiKTeX 2.7, and he doesn't seem to
have an issue with creating the PDF.
Todd