It was annoying but you can root your LG G3 running Lollipop. I confirm it works for the T-Mobile American phone but the comments in the source confirm it works for almost any LG phone.

I followed the same set of instructions on highonandroid.com and on reddit.com/r/LGG3. They really are the same set of instructions but I preferred highonandroid.com because of the accompanying video.

Some issues though:

1. highonandroid.com – I think you need to have SuperSU installed. The reddit.com/r/LGG3 post has this as their first step.
   1. But if you already had SuperSU installed before upgrading to Lollipop, uninstall it and then reinstall it. This will get you to the Lollipop version.
2. Encrypted devices will fail after the Send_Command step. You need to decrypt your device first. There will be output if the step works. No output means it failed.
   1. After running the long command in step 11, you should see “inflate” output shown in their picture.
3. Step 11 on highonandroid.com is one line. Your browser might make it two lines but it is one line:
   1. sh /data/local/tmp/lg_root.sh dummy 1 /data/local/tmp/UPDATE-SuperSU-v2.46.zip /data/local/tmp/busybox

Sources:

1. http://highonandroid.com/android-smartphones/how-to-root-lg-g-flex-2-g2-g3-on-lollipop/
2. http://www.reddit.com/r/LGG3/comments/2ydptk/workinghow_to_lollipop_root/