The 2013 Nexus 7 LTE, now known as the bastard child of the living Nexus family, has not received any updates in the recent round of Android 4.4.3, and subsequently 4.4.4, releases. All of a sudden just now, the 4.4.3 factory image finally showed up, and we can only speculate how long it'll be before we see 4.4.4. For those who are counting, that's 22 days since the Nexus 4, 5, Wi-Fi 7, and 10 have all had their respective factory images available.
Download Android 4.4.3 (KTU84L):
If you are comfortable with flashing factory images, proceed to our guide - you won't lose your data if you follow the directions. Otherwise, hopefully the OTA will be here shortly.
To get a better idea of what's new in Android 4.4.3, hit up this post.