No surprise here. I made a site last year that did almost the same thing as LendInk, but I decided to shut it down after Amazon made it very clear that they didn't want me doing that.
From what I understand, there were a half dozen or so other sites that would facilitate ebook lending, and we were all pressured by Amazon similarly. Most of those sites are no longer around.
Of course Amazon doesn't support it-- they, like the C&Ding authors, subscribe to the kool-aid of "everyone that was lending these books would have been a sale".
Not only do they support it, they actually pay a higher royalty rate to authors who enable lending (making the book lendable is one of the requirements for the 70% royalty tier). If you make the book an Amazon exclusive, you even get paid something when the book is lent (at least for the period of exclusivity).
Just to be clear, LendInk facilitated lending through Amazon, not a service they were providing. They were simply matching users who had the same reading interest.
I doubt Amazon pressured them into shutting down considering LendInk is sending business their way.
LendInk used Amazon's affiliate program. That means (up until Amazon dropped all California affiliates) Amazon would send a percentage of all sales made by that visitor over the next 24 hours to LendInk, as a "thank-you" for sending them traffic.
From what I understand, there were a half dozen or so other sites that would facilitate ebook lending, and we were all pressured by Amazon similarly. Most of those sites are no longer around.