How do I use two different desktops on two different monitors with Lion?
You wouldn't need two VMs running, merely one running while you use the host OS X would accomplish what you want.  It would be easier to give a suggestion based on a more detailed explanation of what you wish to do or accomplish.

If you want something to not disappear when changing spaces try using the "assign to all" option.

From comments below, option for multiple docks

dockit
dockshelf