So the laptop sees that there is a second screen attached but the projector does not see the output from the laptop? Or the laptop only sees it's own screen? Are you using the same cable on the other laptops that do work? Does using another monitor work on the Lenovo?
Try doing a driver update for the video card, Lenovo makes it easy to update everything, run the Lenovo System Update Utility if it's installed, I think it's 5.2 for Win 7 as the latest. If not installed, get it from www.lenovo.com and run it. Great driver update utility.