One HDMI cable transmits both audio and video signal from your 360 to your TV. So if your surround sound system can output sound from your new LG, then you're already set with just your HDMI cable.
If your surround sound system audio reciever isn't setup that way, you could just use the optical audio cable port on the Component cables Microsoft supplied with your 360 to transmit the 5.1 Dolby audio signal. You can get an optical audio cable cheap for $5 online, connect it from your 360's Component cable port (the little black square next to all the video audio wires) to your TV's optical cable input port.
If you're going the latter route you may run into a common problem we all have, that the Component cable interferes with the HDMI port on the 360. In that case, you may find this helpful. Otherwise, if you want to save money, try this free alternative method.
Hope that helped :)
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