Google had recently announced the arrival of Android 5.1.1 OTA update for the 9in Nexus tablet, while the update has actually taken more than four days to appear online as a downloadable link.
However, the good news is that Google has also rolled out the official factory image alongside the OTA update with build number LMY47X, which requires your tablet to be running the Android 5.0.2 LRX22L base firmware as a prerequisite.
On the downside, the massive OTA update (400MB) as well as the factory image are limited to the Wi-Fi only version of Nexus 9 and do not support the LTE variant. So, all LTE users need to wait for a few more days, before they will be able to install the new Lollipop update.
Those interested in flashing the OTA file should use the ADB sideload method via stock recovery, and those looking to install the factory image can follow the steps outlined in the step-by-step guide posted here.
Note: OTA updates will only work on stock firmware without roots or mods. In case the device is rooted, you need to unroot it first or flash the factory image if you modified the base firmware.
[Source: Android central]