Dear Big Picture Big Sound,
How do I get audio out from my LG 42LD520 TV into my Sony home theater system with my TV having no audio outputs?
While your LG TV doesn't have a set of analog RCA audio outputs, it actually does have two audio outputs that you can use to connect it to a home theater system, soundbar or audio receiver. It has a fiberoptic (TOSLINK) digital output -- this is actually required on any television that calls itself an "HDTV." This would use a standard fiberoptic cable, but only if your home theater has an available fiberoptic input.
If you have a cable or satellite set-top box or DVR you could also plug the audio output of that box directly into your home theater system. Again, the fiberoptic or coax digital connection is preferred, or you could use the HDMI output if your home theater system supports HDMI inputs with audio processing.
Hope that helps,