>it probably doesn't hurt to comply with take-down requests //
That would look like some notional acceptance that they were doing something illicit whereas they were merely providing, it seems, a matching service for people wanting to legally lend books to one another.
Where's the RoI for complying with false take down notices?
You can fight it to a point, but that just ruffles everyone's feathers.
As stated elsewhere along this topic, sometimes author's have a moral viewpoint that lending books to complete strangers using the internet violates the spirit of the feature. Look at it from their point of view - they want readers' family and friends to benefit from the lend, but not the wider internet.
Sure, there isn't anything legally wrong with lending books to complete strangers, but working with the author and respecting their wishes can (maybe) generate goodwill that could have avoided getting LendInk taken down in the first place. That said, I don't operate an e-book lending site, so I may be way off base here. Considering that many authors wanted LendInk taken down (and later apologized for it), that's certainly possible.
Anyways, at a minimum, you could provide them with a direct link to their book's admin page on Amazon (if that's possible), instructing them how to disable the lending feature, re-iterating that you'll of course remove their book from the site when they do so.
That would look like some notional acceptance that they were doing something illicit whereas they were merely providing, it seems, a matching service for people wanting to legally lend books to one another.
Where's the RoI for complying with false take down notices?