I have discovered a trick to get the Grado's to work in external audio device connected mode.
You can use the adapter (3.5mm to 6mm). Connect it first let the LG do it's thing and then connect the Grado headphones.
Sounds absolutely superb -detailed, resolution in this external mode.
I can also get some XX jvc headpones I have, in this mode but with a tad more effort.
You slightly push them in not to fully connect with headphone jack remove it and then reinsert and hopefully you will have external mode on.
I have tried with other normal headphones but cannot get it work in this external mode only normal.
Hope this helps
Edit: Just remember the external and high impedance mode triggers the internal amplifier
The normal mode does NOT