How do I create a blank desktop (on OS 10.7.5)
The point of spaces is that they allow for different collections and configurations of application windows, and they do not allow for having different desktops; the desktop is not a window.

The desktop icons shown are simply file and folder items at a file system level that are displayed without requiring to be viewed through an application window. There is only a single desktop folder per user.

Taking both of these into account, what you want can't work for a number of reasons