You can refine the identify filters to include multiple taxa, as well as to exclude certain ones, by modifying the url.
For instance, I can make a url that only shows observations identified in Ascomycota that have not been identified as non-lichen forming classes, and then add to that observations of each of the basidiolichen genuses. Here is a partial version of that:
See How to use iNaturalist’s Search URLs - Wiki to learn more about how to do this.
I agree that looking through observation identified only as Fungi to find lichens would be too tedious, so this is probably the best approach. But maybe you could experiment with searching for words people might write in the description for lichen observations. When I tried it with “lichen”, it was completely useless since it appears that it searches the common name for Kingdom Fungi as well, which is “Fungi (including lichen)”. Changing locality/language settings might possibly get around this.