Old fans can really drive you up the wall with that whirring. I mean, idk, but I've dealt with that grinding noise before. Tried oil on the bearing and it worked like a charm. My buddy used WD-40 on his fan, but that can gunk it up over time. So yeah, basic oil is the way to go. Just a tiny drop, though.
Oh totally, that little spout is a lifesaver for getting oil right where you need it. I had a fan that would quiet down for a week then start up again, just like @nelson.vera mentioned, until I finally swapped the bearing. It's a quick fix once you accept the old one's just worn out.
Wondering if we make too big a deal out of these little noises. Sometimes a whirring fan is just a background hum you start to notice when you're trying to focus. I've ignored that sound for months by just using headphones or, honestly, turning up the game volume. Unless it's a true grinding scream, it's often not worth the hassle of taking things apart (and possibly making it worse).