I had been searching the web and the community forums here for a few hours and finally figured out how to turn off the display on my Macbook Air 2011 running lion and using an external monitor.
With Snow Leopard all you had to do was plug in the external monitor to your MBA then close the lid and wake up the MBA while it was closed. Then you could open up the lid and it would stay off so it would have better air flow and wouldn't get too hot and run the fan all the time.
But ever since Lion, they screwed that up for us.
But after all my searching I finally found someone here give the fix on a MBA.
All you need to do is use a little magnet and put it where the MBA
"I found a solution for this.. my solution is to put a fridge magnet directly right to the return key (about 2 cm away from the right usb port)... so the laptop thinks the lid is closed and so the display is off.. lol.. try it.. it works.."
In this example I used a big yellow magnet just to test it out, but I will be using a small thin magnet for regular use so that it wont mess up my screen if I accidentally close the lid on it.
Also I put a small piece of paper between the magnet and my MBA so that I wont scratch my MBA.
Some will also ask if it is safe to use a magnet on your MBA etc. You are only placing a magnet where the magnet from the lid would go anyway's. Just make sure you don't use a super magnet or something and you should be all good ;-)
Turning off Macbook Air Display when using External Display on Lion