Lippmann photographs are like holograms, specifically reflection holograms. The image is exposed using self-interference, which works in what we would typically consider incoherent light due to a very short distance between the light and its reflection.

Development of the plate produces a superposition of many different volume diffraction gratings mostly parallel to the surface of the plate. If the plate is bleached, these diffraction gratings become high efficiency phase gratings.

For playback/viewing, light from the illumination source is both diffracted and filtered in wavelength by the volume diffraction gratings. In a hologram, the diffraction gives the multiple perspectives that make the medium so cool. For Lippmann photographs, the camera has removed most of the perspective information and the dichroic or interference filtering of the gratings is the primary effect.

In either case, the final image is a layer free image bearing volume in the emulsion.

That's why it can't be effectively copied using 2D techniques. Since the image is 2D (maybe slightly 3D? I'd have to think about that), it can be copied using a standard photographic technique. But the interference gratings in the emulsion have some angular dependence on the light source and viewer's angle that wouldn't be present in a 2D copy. In this way they also look a bit like a reflection hologram.