OTA update is available now, please visit VZW offcial support here to find out software update instruction.
For reference, There are two variants of G2(VS980) launched on Verzion Wireleess: AVRSBK1 and AVRZBK. The update via VZW Upgrade Assistant is available only for AVRZBK version of the G2.
You can use Verizon Wireless Software Upgrade Assistant to update your Software, Since the update is not available Over The Air .
How to Update Verzion LG G2 (VS980) to Android 4.4.2 kitkat
1.With your phone powered on, connect to your PC via the microUSB cable.
2.On your computer you will be notified that your phone has been connected and a AutoPlay screen should display. Select VZW_Software_upgrade_assistant.exe to install the Verizon Wireless Software Upgrade Assistant.
Depending on your version of Microsoft Windows you may receive a warning for permission to continue, select Continue.
3.Once the software upgrade assistant has been installed, run the application. The upgrade assistant will scan for your device and the status will display Upgrade Available. Select Upgrade LGVS980 to upgrade your software.
4.Your phone will restart once the update is complete and the status in the Software Upgrade Assistant will change to Up to date.
For details , please visit LG Offcial Support webpage here.