Alright, I've updated the OP with a new version of IORoot that will let you root your VZW OTA'd G2.
LG is using the F320k-style naming of the unlock file now, so this should do it.
The script now is intelligent enough to know what OTA version you're running and act accordingly.
It should be forwards compatile with new VZW OTAs too, since I've arranged the batch file to fall through the check and just continue on with the VZW OTA root if it's newer than the current OTA, but doesn't match the stock OS version.
If you find that this just doesn't work, let me know.
The old ioroot4 is still available if this causes issues, just change the download link name.