The leap from 5.0.2 to 5.1.1 is not insignificant, so the Nexus 9 had quite a bit to gain from this upgrade. To take another look at those, check out the changelog posts linked below. This release makes a few modifications beyond what we've seen for other Nexus devices, so far. That's what we're looking for in this changelog.
There are only 5 commits separating 5.1.1_r1 (LMY47V) from r2 (LMY47X). One of the changes is specifically for the Nexus 6 (shamu), and another is in the telephony code, neither of which are likely to affect the Nexus 9. There is one commit that changes the platform core of Android, but it only relocates some logic for handling wiped partitions.
This just leaves Flounder-specific (Nexus 9) commits, but they aren't very telling. The first is a change to the build process for boot and recovery images, but it really only affects how Google goes about building and packaging firmware updates. The second commit replaces the bootloader, and it's the most likely culprit for the long, drawn-out delay. Unfortunately, bootloader source code is not publicly available, so we've got no way to find out what is different. We will probably never know why Android 5.1 took two full months to find its way to the Nexus 9.
Like last week's update for the Nexus 9, we're keeping the changelogs split up to show just the completely new commits (from 5.1.1_r1 to r2), and linking separately to the previous changelogs that are also included in this update. Just keep in mind that the latest firmware does include all of these changes, not just the handful of commits mentioned above.