Is it possible to send the audio/video to a 3rd generation AppleTV and close the lid on the MacBook? When I try it, the MacBook goes to sleep. Is there any trick to get this working?
You can prevent your MacBook from going to sleep with NoSleep.
The best thing you can do is turn the Light of the Screen down and use nosleep (or just disable Screensaver and Energysave mode).
On Macs closing the Lid does a hardware Trigger to get your mac to sleep. Don't mess with this because when the Lid is closed the Air-Slices at the Back are covered.
I know one can do this on Windows/Linux Notebooks but you shouldn't do it there either cause they will also overheat.
Overheating (as some people say) is not an issue when the MacBook is closed. It is constructed to also be used in a closed fashion, it only sleeps with a closed lid when there is no external monitor and input device connected as Apple notes in their knowledge-base article:
There are several free tools that keep the mac awake when closed. I use InsomniaX