(I have no clue whatsoever) How do you identify it as lichen and not, say, fungus or slime mold?

Good question! Many ascomycete fungi have disc-shaped fruiting bodies, but only lichens have a thallus (the flat bit) with algal cells in it. Often there is no visible thallus in asco fungi. With this one I can see a pale green granular thallus.

Here is Kelleromyxa fimicola, my favorite slime that lives on dung. The plasmodium is a peachy color, and probably would be difficult to see on the dung. I've never seen it in person

Fungi and slime molds both grow on dung and the fruit bodies may appear similar without a microscope. Slime molds form acellular fruit bodies and mobile plasmodia while fungi form multicellular fruit bodies and mycelia. I haven't heard of any lichens that grow on dung but I'm no expert