Overdrive (the service most libraries use to lend out books to their users) uses Adobe DRM if you read the book in Overdrive's own app on iOS.
I have an iPad1, so I'm probably screwed. I'll still be able to use the Kindle app to read borrowed books, but some books don't allow reading on Kindle.
We use Overdrive from our library on two separate Android devices. Does not worry me for my device but the other user is not technology adept. Just getting Overdrive working and the user trained on was a nightmare and bucket of frustrations.
I have an aging (5 yrs old) Sony reader that I still use. It uses Adobe DRM, but it didn't when I first got it. Sony have been pretty good about updates so far.
If DRM breaks for it, then I'll simply stop buying books from the Sony store (which I mostly have already) and just use DRM-free ebooks from gutenburg etc.