I have not made or seen Lippmann emulsions, but I am a physicist. You don't need a metallic mirror to get a strong reflection (jewel beetles and morpho butterflies do very well with lamellae of chitin and air). However, the silver lamellae in a Lippmann emulsion are created with a metallic reflecting surface on the back of the emulsion, and it seems clear that reproducing that metallic coating will maximise the wavelength-specific reflection when viewing. The phase shift when light reflects off the back of the emulsion will be the same with or without a metallic layer, but the strength and wavelength dependence will certainly be different.
Black you get by destructive interference. The light is either absorbed, or scattered to non-viewing angles.