I would love to see the lobby of the library overhauled so that its front on the Library Green is mostly glass (or shatterproof windows) with more doorways and a patio there. A coffee shop could operate in that transition area from the park to the library, creating more of a porous border, and a social scene.
This is what I picture: A coffee shop, hangout for people walking into and out of the library. There would be some shelves of used books -- as there are in the lobby now -- for purchase, or just for perusing while killing time there.
It would have a view onto the green, and could be a great place for people-watching and viewing events that happen there.
The way I see it, there would be a moveable wall back by the checkout and drop-off desks of the library, so that it could be closed off. That way, the coffee shop might continue to operate a little later than the library, and could be open other hours when the library isn't, even on holidays.
When there is an event at the Library Green, like a concert or a movie night, the coffee shop could stay open at the same time.
That might mean losing some plants and some of the space for art in the lobby. But the plantings could be added elsewhere, and the art space could be reconfigured. In fact, it would be there to give the coffee shop patrons something to look at and talk about, giving greater exposure to the artists.