Hi, I had this problem too on my new G3 (now running Lollipop with the OTA update). I tried a bunch of things but Android Device Manager on the web could
not locate my phone -- the error was always "Location unavailable".
I suspect this is because of the fact that I had 2 Google accounts on this phone. (Both accounts had Location Reporting on, though.)
I used to have 2 Google accounts, one for my contacts and one for everything else. I got rid of the contacts-only Google account because lots of Google apps (e.g. Play Store, Play Movies, Google+) seemed to think that was the default Google account on my phone.
After deleting the contacts-only account, the Android Device Manager website began to report the location correctly.
There's no reason Location Reporting should not work with 2 Google accounts -- my old phone running stock Android 4.2 managed it fine. This is probably a bug with LG's version of Android.
My location settings look like this now:
