2013-05-31, 10:41
VLC will be using the Windows default sound device which is shown by the green tick, which for you is the LG TV.
XBMC should also show the LG TV in the list of devices, however it's missing from the XBMC list this is why you are not getting audio out from XBMC. The only reason I can think of is XBMC is not detecting the TV as being on, so please make sure the TV is on before starting XBMC otherwise it won't be detected, as the routine for detecting audio devices is run at XBMC startup.
XBMC should also show the LG TV in the list of devices, however it's missing from the XBMC list this is why you are not getting audio out from XBMC. The only reason I can think of is XBMC is not detecting the TV as being on, so please make sure the TV is on before starting XBMC otherwise it won't be detected, as the routine for detecting audio devices is run at XBMC startup.