There is now a better, faster, and simpler way to root your G2, thanks to one of our favorite Android hackers, Justin Case, and it will work on all LG variants.
Download and install the app from this XDA Developers thread
Open or run the Stump Root app you just installed
Click the “Grind” button, which actually roots the LG G2
Reboot your phone once instructed
Install SuperSU APK from market
Download joeykrim’s very popular Root Checker app from Google Play, which verifies whether your device has root or not.