Just like the recent Galaxy devices from Samsung, LG has included a root checker on the G3, which will automatically trip if it detects that the handset has been rooted, effectively voiding the warranty of the device.
Usually in these cases, users have to wait until a developer manages to find a way to bypass the root checker or an exploit in the firmware that would give them root access.
The G3 comes with a “bnr recovery” mode, originally found by IOMonster, under which the system and data partition are mounted in R/W. Pushing a pre-packaged tar file from the developers using ADB under this mode containing SuperSu, daemonsu and the install-recovery script will then automatically root the handset and also prompt them to install the TWRP custom recovery. Simple, isn’t it?
There are a couple of bummers though. The method will not work on the Verizon and Sprint variant of the G3, and for now the developers have only released their pre-packaged script for Linux and Mac owners. They are, however, actively working on bringing a version for Windows users as quickly as possible.
The developers have also compiled a list of G3 variants which are compatible with PurpleDrake, which can be found here. The rooting instructions and the download link for the necessary files can be found on this XDA thread.