Well, that took a bit of sorting. Turns out it has nothing to do with either LyX or LaTeX; it's something sneaky in your image. Your screenshot is 296x296 pixels, which sounds (and looks on the desktop, or in an image viewer, or in the LyX GUI) square. The catch is that the resolution is (rounding a bit) 1024 ppi (pixels per inch) horizontal v. 768 ppx vertical. 296 px at 768 ppi is more inches than 296 px at 1024 ppi. So the "distorted" PDF output is technically correct.
You can, of course, set both the height and width to equal values in LyX and force a square image. I also converted your image (using GIMP, but other image editors can probably do it too) to 296x296 px at 768x768 ppi, and included that in the document while setting just the width. That worked too. Paul
