MacOS – I can’t install OSX Lion from DVD, because I receive an error

If you copy the CD to a disk image on the PC, you can put the image on a USB stick and transfer it to your Air. I am not sure how to do this on Window, but I'm sure you can find out how to do this somewhere.

WinImage looks like it should do what you want.

Also look at this article on creating CD images on Windows.

It's hard to know where the failure lies, but you might be able to get around the issue by re-installing Snow Leopard from media and then running the installer you have saved on the DVD/USB. This will avoid having to try the "official" Lion install and see if your installer is the cause or the mac has issues of it's own.