if I think I’m going to store it for a while, I spritz it with rubbing alcohol and wipe a layer off with a tissue. then I just keep it in a cool, dry cabinet. if you’re extra worried, maybe the fridge is a good idea.
this is probably going to sound kind of weird and maybe ill advised, but I’ve kept some lipsticks for a really long time (like a decade) and never had an issue. I always wipe a layer off again before using.