Hello again,
Now PNG does support transparency, so you should be able to get this to work -- but only if you use pdflatex to output PDF as your finished product. Printing directly from LyX generates PostScript, which is then printed.
This is exactly what I wanted to achieve - thank you both ever so much for your suggestions! Much easier than I expected it to be too somehow.
Kind regards, Dawid 'Another Happy User' Ciecierski