I think it's an excellent idea and something I was thinking about and researching a couple of years ago. The idea of an internet lending library is to make books available to folks across the internet and overcome the geographic limitations and restrictions of a local, public library system.
Fictionwise has set up something similar to what you describe, but their collection is quite limited. If you belong to Fictionwise's Buywise program, then you can check books out of their library. When I was exploring their site to learn more about their program I think I remember seeing something along the lines of, "if their lending library does not have a book you want to read, you can purchase it from them at a discounted price and then immediately donate the book to them," but I can't find anything about that now on their website.
The problem I see with the concept is how one would transfer the DRM rights for a book to a lending library. With Fictionwise's model, any books you'd want to donate to the library would be bought from them and donated to them before the book is read (essentially, you never own the book). Then after the book is donated, you can check the book out of their library.
Fictionwise
licenses their lending library technology called Libwise to libraries for this purpose.