No, HD can't be carried out of a cable box on coaxial cable. Or, more accurately, cable boxes could be designed this way, but are not.
You may use one of the following types of connections to carry the HD video:
HDMI
DVI
Component
Those 3 are the only way to come from your cable box to your television in HD. If your LG box (MODEL #???) has HDMI inputs then this is a good way to get audio and video to your TV. If it doesn't have HDMI then you must run audio (coaxial/optical digital) from the cable box to the LG system then run the video separately.
If the LG doesn't have HDMI, DVI, or component video inputs, then you have to run the video directly to the TV.
If you want to use HDMI/DVI and your TV only has one input, and you need more, then pick up a separate HDMI switcher (5x1) at
www.monoprice.com