You could test these hypotheses by identifying the fungi in each kind of lichen and seeing where they fall on the phylogeny of fungi. If Hypothesis 1 is true, then lichens in each group should fall into different fungal phyla (or groups at other taxonomic levels). If Hypothesis 2 is true, then no such relationship should exist.
Work Step by Step
The key here is to see that the hypothesis are opposite ideas which depend on the taxonomic position of the fungi involved, which implies the need to find out which phyla the fungi from different kinds of lichens fall into.