I'm not sure how it's done on a 2011 Tour but on a 2017 Adventurer you have to use the TV remote to set the audio to external output and you have to set the LG Home Theater to Aux input.
I think it was detailed in the Operator's Manual. Here's a link to a PDF of your Operator's manual:
We did it once or twice for watching movies but if you're trying to do it to improve the sound or hear it better over the sound of the A/C I wouldn't be to hopeful that it will help. You'd probably do better with a separate Soundbar installed on the TV.
I just checked your Operator's Manual and it's in the Entertainment section of the manual, Section 8.3: