I don't know of any public libraries that handle their own general ebook lending. They use services like Overdrive, and in the case of Overdrive how the actual ebook file is served depends on which type of ebook it is. For ePubs, the file is downloaded directly and managed with Adobe Digital Editions (Overdrive's ePubs are generally all protected with Adobe DRM). For Kindle books, the Overdrive site directs the user to the Amazon site (with some kind of authentication token) where the user can have the book sent to his/her Kindle device.