That's a completely different system where Amazon themselves "lends" the book to Prime members only. LendInk allowed people who bought Kindle books to connect with people with which they could use their "lend to anyone you like" feature, which is included as part of the "purchase" of the Kindle book.
In some cases, Amazon went as far as to simply buy a copy at full price and then only give access for the regular lending period to promote the Kindle Lending Library, but that was only for high profile books like The Hunger Games where they couldn't strong-arm the book publisher to agree to better terms. If this doesn't sound like it makes sense, think of it as a loss-leader for Amazon Prime for Kindle (device) owners.
Thanks for explaining this scenario. Is there no other scenario where an indie author would receive compensation for lends of their books facilitated by LendInk?
An Amazon KDP published indie author would only gain possible exposure through this system, and never direct compensation. That said, as an indie author I like the idea of LendInk and would be happy if people were buying my novel and then sharing it there: it would mean there was interest in the book and it would mean reaching more readers who would potentially seek out more of my novels and become potential future customers. I actively gave away hundreds of digital copies of my novel over a 24 hour period to gain exposure, so I have no beef with a site like LendInk.
