Late Yesterday, Google unleashed some sweet Lollipop goodness on the whole Nexus community, including the Nexus 9, which got a small - yet significant - bugfix update that improves performance. However, it seems like the OTA update to LRX21Q (the new build released yesterday) isn't working for everyone. Here, I'll try my best to explain why that might be and how you can get this latest update without waiting for Google to release another OTA to fix the issue.
When your Nexus 9 came out of the box, you might remember that you needed to update your software before you could get started, this took the Nexus 9 from build number LFW73W to LRX21L. It seems that for some (at least it doesn't appear to be happening to everyone) that original update out of the box didn't upgrade the Nexus 9's recovery, which is why some people are getting an error when they try to run the OTA update to LRX21Q. If you're still with me at this point, it basically looks like some Nexus 9s are still using an outdated recovery, and when the OTA from yesterday checks for a newer build, the update fails.
If you really can't wait for the latest update and you want that performance update, you can go ahead and flash the latest Factory Images - which we outline here - and if you want to keep your data, you'll need to follow these instructions carefully. First of all, you'll need to have adb and fastboot set up on your PC or Laptop and if you don't know what I'm talking about, then maybe you should wait. From what I can see, this latest factory image doesn't include an img that wipes your data, but I wouldn't quote me on that. In fact, I would be prepared to restore a previous backup of your device.
If you don't want to flash things manually, then you might want to just wait for Google to release a fix for this latest OTA mixup.