I found a library that on their website mentions that they sell new books in their bookshop. I have seen numerous libraries that have a bookstore inside them that sells used books but have not seen many that sell new books.
From the website:
The Library Bookshop, a concept pioneered by the Drayton Valley Municipal Library, is continuously expanding service geared toward the specialized need of our users. We retail new books to our customers at discount prices. If you have a book you would like to order, call the library and place an order. Delivery is dependent upon availability and the timing of our orders.