When I plugged my MacBook Air running Lion into a projector today the projector only displayed the desktop background. I could swipe between desktops, but it still only displayed the background (this was particularly weird for the dashboard where it showed the dashboard background but not the widgets). When I opened system preferences that window displayed, but nothing else. Any idea what happened or how I can fix it if it happens again?
Have you tried running the mouse over to the left/right corners of your MBA screen? It should jump onto the projector screen - I think Lion is default for ext. screen to be on the left.
You should be able to drag any app then over to the screen in the same way the mouse passed across.
Where the big screen is compared to the little screen can be configured in System Preferences > Display > Alignment.