I recently found an insect (a helpful expert on iNaturalist suggested it may be a nymph member of Psocodea) eating an Evernia prunastri specimen I was looking at under a microscope. So they definitely can be a problem! I immediately put the thallus in my freezer for a week and didn't see them afterwards. I've read alternating freezer and room temperature can be even more effective as well.

That said, I'm new to collecting too-- I'd love to hear from others who have more experience.

For home lichen collections I agree with Daphne. I have not seen lichen herbarium collections deteriorate from grazing insects. But if you are affiliated with an institutional herbarium, you should ask the collections manager or director about their policy for freezing botanical specimens. At the University of Washington, where I house my lichens, I have to freeze them for 48 hours, regardless of what I think about freezing.

At the University of Bergen, in Norway, Tor Tonsberg freezes all lichen collections for a week, before storing in their herbarium. It is all a matter of where your collections are and the policies of the institution of where your lichens are stored.  If storing at your personal considerations home, you get to decide.

I have seen silverfish in the UW herbarium eating labels. They like the glue that was used on older packets. 

Katherine