How do I use two different desktops on two different monitors with Lion? So I want to use two different desktops on my two different monitors in Mac OS X Lion. The only options I can find are extended desktop and mirror desktop.

Is there any way to use two desktops simultaneously and pin one to each monitor? Either a native OS X functionality or (cheap) third-party solution?

The reasons for desiring this are essentially so I can have the two monitors functioning completely independently of each other. I would like two menu bars (the program SecondBar achieves this to a limited extent) and two docks (I haven't found a good program to do this). I would also like the ability to, for instance, play a game on one monitor while have the other free for browsing and typesetting.

(I have considered using a VM program like Parallels or VMware to create a second instance of OS X and pin the VM to my second monitor, but I would like something a little less memory intensive if at all possible.)
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