As I understand it, as soon as the IA makes the digital copy they want to lend (digitally or physically), they now have two copies of the book and have committed copyright infringement. As soon as they lend a copy, there are now three copies in existence (unless they delete their copy as part of the loan) which is another count of infringement.
If they had a system where every page of the original was burned as it was scanned, and when you "checked out" a book it literally deleted the original on the server as it was sending it and the person returning the book also transferred the bytes back it would be quite a show.
I'm about 95% sure a scheme like that would still find them shut down. Remember the Aereo decision? They went through similar contortions, including building an antenna farm with thousands of tiny individual antennas, and were immediately killed off by the courts because it was seen as a legal hack. Such a scheme might threaten cable TV income if it were allowed to stand. Protecting incumbents from competition is a vital role of the courts.
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See also Peter Sunde (of Pirate Bay notoriety) and his “Kopimashin”: https://www.engadget.com/2015-12-21-peter-sunde-kopimashin.h...