Do the organisms within a lichen communicate with each other?
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 &amp; Athukorala 2017 a helpful place to begin learning more.

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