Something like this would do the trick probably:
http/www.newegg.com/Product/Product.aspx?Item=9SIAAFF5339492&cm_re=optical_to_headphones-_-9SIAAFF5339492-_-Product
No guarantees on audio quality. However it looks very similar to a unit I use for optical -> analogue input into my speaker system at home. It's probably got the same active components to my unit. It runs into a decent-ish Sony Amp and speakers and it sounds pretty good to me. Having said that, while I appreciate decent sound, I'm no audiophile. I'm sure someone with good ears and nice equipment wouldn't be caught dead with a unit like that in their system.
But for $19 it might be worth a shot.
It's stereo only, so you need to make sure your LG TV can be configured to output 2.0 audio on that optical link. It won't handle a 5.1 or similar output.