Interesting question. Apparently, yes for both taxa.
Doing a brief scan on the interweb revealed these sources. I cannot validate the accuracy of this information. Interesting topic though. I imagine that crustose lichens would be easily fossilized as oppose to the soft thalli counterparts. There's probably some encased in amber or impressions in certain rock through the carbonization process or casts/molds of buried organism.
https://ucmp.berkeley.edu/fungi/lichens/lichenfr.html
https://nph.onlinelibrary.wiley.com/doi/10.1111/nph.12009
https://ucmp.berkeley.edu/fungi/fungifr.html
-Lin