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.