For your information, the previous firmware update for AT & T LG Optimus G (LG E970) is “V10o” revision “00_2”.
AT & T LG Optimus G (LG E970) users can download and install the LG Mobile Support tools to upgrade their devices.
How to update Sprint LG Optimus G (LG LS970) firmware with LG Mobile tool.
1) Download the latest USB Drivers for your LG Optimus G.
2) Download LG Mobile Support Tools Here.
3) Install LG Mobile Support Tool to your PC.
4) Launch the LG mobile Support tool from PC.
5) From LG mobile Support tools screen, choose country and model (LG E970)
6) Connect your device to PC via USB Cable.
7) From LG Software Screen, Click Start Updating.
The tool will analyze the phone environment, i.e., check connection status with the phone.
wait until the update process is finished.