For math equations with instant preview turned on, the equation graphic in LyX 1.6.7 is rendered with some fixed background color (salmon, I think, on Windows) even if it's in an inset (e.g., LyX Note) with a different background color (yellow). I don't know the details of the preview mechanism, but in web design one would solve this by using a PNG or a GIF with alpha transparency for the background. PNG is preferable for rendering text.