You can use the LG mobile Support tool to install the latest firmware update.
You can Download the ‘LS970ZV9’ firmware for LG OTPIMUS G (Sprint) LG LS970 smart phones.[LS970ZV9_02.SV9_02.P25006.cab] and covert it to LG Firmware .kdz File and Flash the ROM by yourself.
If your device’s current firmware is “LS970ZV8”, you should download and install the LG Mobile Support tool to upgrade your device firmware.
By the way, the Open Source Code Distribution for LS970(Optimus G)_Android_ICS_LS970ZV9 is available too.
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 (LS970)
6) Connect your LG Viper to PC via USB Cable.
7) 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.