The rapid phylogenetic placement and molecular barcoding of fungi is often hampered in organisms that cannot easily be grown in axenic culture or manually teased apart from their associated microbial communities. A high-throughput procedure is outlined here for this purpose, and its effectiveness is demonstrated on a representative species from an especially problematic group of fungi, the sterile crustose lichens. Sequence data of the LSU and ITS regions were generated from samples of a sterile crustose lichen species, Lepraria moroziana, using next-generation sequencing. DNA fragments most likely to represent the primary lichen-forming fungus were bioinformatically teased out using a specialized data processing pipeline. Phylogenetic analyses of the LSU region revealed that the lichen-forming fungus L. moroziana was previously placed in the incorrect class of fungi (Lecanoromycetes), and actually belongs to the class Arthoniomycetes, in the order Arthoniales. It is here treated as a member of a new family (Andreiomycetaceae Hodkinson & Lendemer fam. nov.) and genus (Andreiomyces Hodkinson & Lendemer gen. nov.). Additionally, Lepraria obtusatica Tønsberg is placed in the newly-defined genus based on its morphological, chemical, and ITS-based molecular similarity to L. moroziana. The procedure outlined here is projected to be especially useful for resolving the dispositions of diverse problematic fungi that remain unnamed, incertae sedis, or have taxonomic positions that are not expected to reflect their true phylogeny.