Do the organisms within a lichen communicate with each other? So you've got your fungus and your algae (or cyanobacteria) (and the multitude of other variations and additions to this two-species symbiosis that lichens present). Do the species that comprise the lichen communicate with each other via chemical or electrical signalling? For instance, could an algal cell "tell" the fungus that it's diseased, thus triggering the allocation of more resources toward pathogen resistance? And if there is no communication, how have lichens been so successful?

Communication definitely happens, but I don't know of any research into response to disease.

One example are molecules known as lectins that help the fungal partner recognize the correct photobiont (algal or cyanobacterial) symbiont.

Another example are the physical connections between fungal hyphae and photobiont known as haustoria that appear to help the fungus extract sugars from the photobiont.

You should find this review by Piercey-Normore & Athukorala 2017 a helpful place to begin learning more.

Ref: Piercey-Normore, M. D., & Athukorala, S. N. (2017). Interface between fungi and green algae in lichen associations. Botany, 95(10), 1005-1014.