Looks like one of those old National locks. They were designed to be replaced, not repaired, but the company went out of business a very long time ago. The National Cabinet Lock division is still around as NCL, but that won’t help with this.
I would just install a new privacy lock. The new locks are larger and will cover up the holes of the old one. I haven’t done residential work in years, but I think various brands make privacy locks with glass knobs.