Just looked at the cable box specs on the Cisco site and it showed HDMI 1.3.
Both your cable box and LG unit are HDMI version 1.3, or should be. So in theory your set up should work.
However I suspect that the cable company has installed old firmware in the box.
Unfortunately we get a boat load of HDMI problems with cable boxes. It is not helped by the fact that the cable companies appear to have a poor grasp of the problem, and are happy if the box gives a picture when connected to the TV.
I suspect you will have to lead them by the nose and ask about available firmware updates.
I would try another good quality HDMI cable just in case that is the problem. Not all HDMI cables have the required bandwidth.
After reviewing your cable box and your LG unit, and past experience with other posters problems, I feel this is most likely a cable company issue. We have had quite a number that only work with direct TV connection. However when members are persistent with the cable company they usually get satisfaction.
I don't see any updates to download for your LG unit, but if all else fails you might ask LG if there is an update you need.
Unfortunately HDMI is a needlessly complex system with a lot of versions and even more addenda within versions. So we do run into compatibility problems, but I don't think as may as we used to a little while ago.
I think this is as far as we can take your problem on this forum. Good luck!