I went to http://www.lg.com/us/support-product/lg-47LM8600 and clicked on the software update there on my laptop.
I see some zip file and a document called "Software_Upgrade_Guide(English).pdf" which appears to be another way to update this.
You bring up a good question about these TVs. It's an appliance, not a computer?
I'm on version 04.00.17,and I'm trying to use WatchBig! by LG from my Samsung Galaxy Tab 2 10.1 GT-P5100 running Android 4.1.1 , which demand the version 04.12.21 or higher.
I've tried the software update menu from my TV, but it says there's no update available, I've checked the connection, and it's working.