First sale doctrine doesn't apply between conpanies no. When it's two companies, and both libraries and authors are companies, then the contract terms apply. There are no consumer protections between them. That being said, I don't mean necessarily in terms of public lending rights as some countries have but rather that a book has a limited lifespan before it falls apart and library has to buy another copy. They can't just print out missing pages and stuff like that. So there is that cost of buying (and library books tend to be more expensive because sturdier binding and pages), divided by number of times it was able to be lent out.