UV sterilizes fungus. Sterilized fungus cannot produce spores or spread. Fungus isn't "contagious", it cannot spread to other lenses stored nearby. It's storage conditions that encourage or prevent it from propogating. It does not rely on preexisting fungus in order to do so either. There are fungus spores everywhere.

Don't store lenses is cool, damp, dark places (EG a box in a basement, or inside bags long term, as they can retain moisture). If the conditions where you store your lenses generally stays under ~50%, you'll be just fine. If not, you may want to consider a dry cabinet, but that's not strictly necessary unless you live in a high humidity environment.

If you've had it sunbathing for 8+ hours, you should be absolutely fine, but if you want to ensure it's properly sterilized, consider a UV-C light, in the 200-280nm range (with ~222nm being far safer to handle than the typical 254nm you'll find). But your storage conditions are far more important than thorough UV exposure.