The Library Law Blog asks this question and pretty much decides that the library probably can’t.
According to the licenses that come with the iPad you cannot “rent, lease, lend, sell, reidstribute or sublicense the iPad Software”. By lending the iPad to a patron the library is also lending the software, which is prohibited.
As to the Kindle, the Kindle license allows use of the digital content on the device “solely for personal, non-commercial use”. Of course a library is not making “personal” use of a book that it buys on a Kindle for lending purposes.
What’s a library to do?