Can we buy licenses for e-books and lend them to students?

Generally speaking, when you purchase digital content, you are usually purchasing a license for said content. You will have to read the license to find out what the terms are. For example, here is the general license agreement for the Kindle store. It states that as a general rule:

Unless specifically indicated otherwise, you may not sell, rent, lease, distribute, broadcast, sublicense, or otherwise assign any rights to the Kindle Content or any portion of it to any third party

which would prohibit the scheme you suggest in the general case ("unless specifically indicated otherwise").

Similarly, for books sold in the Google Play store, the license terms include the following:

You may not lend or co-own any of your Books on Google Play purchases with another person.

The specific license terms can vary by content distributor, publisher, and individual book.

In cases where lending is permitted (e.g. some Kindle books), it's usually very restricted - for ordinary customers. Libraries can purchase licenses for some books that are more permissive for lending purposes. You should consult with your university librarians about what options are available to them.

You may be able to find an appropriate book for your purposes with a permissive license that allows lending (maybe even some open educational resources, if you're really lucky), but this will probably take some work.

One of the problems with how software is licensed, is it is not always clear when you are violating the EULA. After consultations with our library and IT department, we bought a large number of iPads that students can borrow from the school. We have loaded these iPads with a number of useful books, including our core textbooks. The IT and the library felt the issues with iPads were less than with lending the ebook directly or using laptops. The issue with laptops is that each user would generally have a separate and private account while for an iPad there is only one account. Your best bet is to talk to someone else and get them to sign off on it.

My guess is that your best chance is to do this via your library (not as institute).

Here's is a localized answer for ebooks and libraries for Germany:

Source: http://www.bibliotheksportal.de/themen/digitale-bibliothek/e-books-in-bibliotheken.html

• The UrhG (German copyright law) has explicit rules for content on physical media. Besides printed books this also covers CDs and DVDs.
  Roughly speaking the idea is that a library is allowed to lend out books on physical media. The loss of the publisher because of a larger number of readers for the book is compensated by a so-called "Bibliothekstantieme" ("library royalty").

• The problem with ebooks is that they are not covered by those "physical" library rules. This means that libraries negotiate individual licensing contracts with the publishers.

• The university library ebooks I've used so far were restricted to reading from university IPs, some even to computers at the library. Look&feel of the procedure were similar to electronic journal access.
  Talk to your university library, I'm sure they know how to deal with that. They'll probably also be able to give rough guesstimates about the costs.

• There exist public e-libraries, e.g. Onleihe is an network for ebooks of public libraries mainly in the German speaking countries. They know for sure how to deal with this, and something the like probably also exists in your country.

  The mode of this is described (I haven't tried it personally) as very similar to traditional library use: there is a number of copies available, if they are all lent out you have to wait until one is "returned". You get access for a restricted time and then the reading license is returned and you cannot open the book any longer.