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you can do png images if you use a package like graphics or graphicsx and process the .tex file with pdflatex.
Yes, and if you would rather stick with normal LaTeX (I have no idea if lyx supports pdflatex) then all you have to do is convert your PNG to EPS first (I tend to use a makefile for this but there is nothing to stop you doing it by hand). It is best to omit the file extension when including the graphic, then you can use the same source with either LaTeX or pdfLaTeX. LaTeX will then look for a .eps or .ps file of the image, while pdfLaTeX will look for a .pdf, .png, or .jpg file. The order of search can be customized of course, and it is possible to define custom handlers that will, for example, automatically convert PNG to EPS before inclusion (although this may give you problems with bounding boxes).
Be warned, however, that there are a million-and-one bad ways to convert raster images to postscript and only a handful of good ways (by which I mean no degradation of quality or excessive file-size inflation). In my opinion, the best solution is imgtops: