What you describe as lending a digital copy, is making new copies. As a matter of engineering fact, the bytes were copied from one location to another; as a matter of black-letter law, that is making a copy in the sense that it is copyright infringement to do so without a license. That IA 'controlled' it to have only one outstanding copy at a time in hands other than theirs does not make it legal. The carveout saying libraries can make three copies does not cover them making hundreds.
If IA would like five dozen copies to be morally equivalent to one copy as long as they ask each person who received one to swear they deleted it before IA makes another, they can call their congressman and ask them to propose a copyright law amendment. They did not do this, and instead just knowingly violated the law repeatedly. Wailing about how libraries won't exist in the future is silly, because it just takes reforming the law to fix this, but IA seemed to be under the impression that as long as the rules would one day be amended, they could act as though they're already amended that way today.
Let's say we have a device that allows to view book pages over Internet without persistently storing it in any tangible medium (like a memory card). I.e. without "fixing" it permanently where "fixing" is defined in 17 US Code 101. And we use it to view books from a remote server. In this case it seems like we are not making a "copy"; we simply let user watch book stored on our server. So this should be legal?
As in, is it somehow different when the copy that gets transmitted to the user's computer is encoded images of the pages instead of encoded text of the pages? No. You are using the word 'view' to describe receiving a copy. Again: It doesn't matter whether the UX presents it as a copy. The data factually is copied, and that's all that matters.
There was a company that allowed customers to rent DVD players, robotically inserted disks into them and transmitted their video output over the internet.
This was ruled illegal.
The letter of the law isn't the real law; the real law is that you must pay money to large media corporations or else. We now have two instances.
That doesn't solve the fact that the robot can't do the reading for the user. It takes a picture (makes a copy of the page), then sends a copy of that data to some remote user (distributes an infringing copy).
It does if the copy is "more than transitory". Software in RAM is a full copy and remains there as long as the program runs, so that can be an unlicensed copy per MAI v Peak (but if you had a license to the original, there's an explicit legal carveout for RAM copies). It would depend on how far the data is buffered and how long it is cached.
If IA would like five dozen copies to be morally equivalent to one copy as long as they ask each person who received one to swear they deleted it before IA makes another, they can call their congressman and ask them to propose a copyright law amendment. They did not do this, and instead just knowingly violated the law repeatedly. Wailing about how libraries won't exist in the future is silly, because it just takes reforming the law to fix this, but IA seemed to be under the impression that as long as the rules would one day be amended, they could act as though they're already amended that way today.