Just yesterday, Google made the official factory images for the Nexus 7 LTE (2013) available to the public. (Actually, they made quite a few factory images available.) Just one day later they have already started pushing out the update to the device.
They have yet to specific what changes Android 4.4.4 includes, but we know at least that there is a smattering of carrier-specific radio adaptations, bug fixes, stability improvements, security enhancements and speed optimizations.
For the impatient/antsy folks, you can go to “Settings,” then “About Device,” and select “Check for Updates” to manually get the upgrade.
Enjoy!