Is there a way to recover lighting conditions from a render?

I’m trying to replace an object in a rendered scene with a 2d image of an object of the same shape but different texture. I know all the rgb values of the existing image without the lighting effects in the image. Is there any way to create a mapping from that difference which I could then use on my cg image to give it the same lighting effects i.e. hue, saturation, shadows etc