I have done some research on it and it seems none of the LG LCDs with usb port supports Divx with HD resolution (neither 720p nor 1080p). To play HD content you have to purchase an external HD media player like the Western Digital TV HD Media Player.
Yes, it plays them on my LH70. I remember reading a forum post on AVforums where a guy had managed to play hd content over his USB in LH30 and according to replies there this service menu hack works on all LH30-LH70. Just find that thread and you could save your spending on a digital media player like many others. Let us know if it works.