Which models are you working with? For all components please. That's the only way we can be 100% certain about what you are working with. There are some subtle differences in connections/options/ports between them, mind you (e.g. some directv boxes lack HDMI, or lack Component outputs/Some all in one type HT systems lack ample HDMI inputs, etc.)

That said, this is how I usually recommend someone connect the 'standard' components such as what you have listed (cable or sat box/receiver/speakers/hdtv). I've listed a few options, given potential limitations of available ports/connection types on each component. Baseline is that you would like surround sound options for all inputs, eh?

DirecTV receiver (HDMI out) --> (HDMI in) LG Smart Blu Ray HT system

LG HT system (HDMI out) --> (HDMI in) Sony HDTV

OR

DirecTV (HDMI out) --> (HDMI in) Sony HDTV
DirecTV (digital optical or digital coaxial out) --> (digital optical or digital coaxial in) LG HT System
LG HT System (HDMI out) --> (HDMI in) Sony HDTV

OR

DirecTV (Component videoout) --> (Component video in) Sony HDTV
Direct TV (digital optical or digital coaxial out) --> (digital optical or coaxial in) LG HT System
LG HT System (HDMI out) --> (HDMI in) Sony HDTV