Well, the fact that it is in Index Fungorum and not in Species Fungorum suggests they haven't decided where to put it, so that seems a bit dubious to me. The source of the synonymy listed in CoL (Denkschr. Akad. Wiss. Wien, Math.-Naturwiss. Kl.Vol.: 104 p. 341) might be valid. Hard to follow up on it, though.

I would suggest to swap L. parmelina to L. epibryon ssp. broccha, some sources following Lumbsch's view from 1994.
"Species Fungorum" does not list L. parmelina, as Ken-ichi says, L. epibryon is listed but without subspecies'.
"Index F." lists parmelina without referring as synonym to epibryon ssp. broccha, and lists some vars. and ssp. of epibryon.
In this case the Index is obviousely the updated source, but misses to include treatement by Lumbsch et al. 1994, reporting parmelina as synonym.

Our approach here would be to wait for Index / Species Fungorum to update, since they're our fungal authority. That way we don't have to argue over whether or not Lumbsch's treatment is correct or not.

Well, I recommend we just leave it here until Species Fungorum adds it. lg_price, it's not clear to me if mycobank is just a nomenclator or if they have opinions about what the current names should be, but either way they are NOT our authority when it comes to fungus. We follow Index/Species Fungorum, so when they update, we can update.

No, just leave it. If people want to use it before Species Fungorum figures it out, let's let them. It's not really doing any harm.