I called their customer service on 12/22/12 and was told that LG is working on the App software for amazon instant video for my 47lm7600 model. The impression I got from the conversation was that most if not all of the smart tv's will have this updated in the future. He couldn't tell me exactly when. Right now this feature isn't available on any LG tv if I understood him correctly.
I was surprised and dismayed that this fact wasn't highlighted in the product description. There is a workaround. If you have an XBox 360 AND you subscribe to XBox Live Gold, you can add Amazon Instant videos to your apps. Pricey, but it works great!
I cannot stand how Amazon and LG do not play nice together --- I actually returned a Sharp TV after I found (after the fact) that it would not stream Amazon Prime.........I then went and bought an LG after a sales person guaranteed that LG and Amazon were compatible (and many devices were in 2012) -- but, lo and behold -- I get my LG TV home -- and, it also is NOT compatible........unreal!!!!! I have to keep returning TVs......this really sucks........why cannot they not simply all play nice together.............I am going to get rid of Amazon Prime now, as this is a total joke....and, screw LG too........technology sucks!