Currently it isn't possible to have two different instances with different settings running. This is because the settings like the currently selected driver and driver settings are saved to the windows registry so that each instance would overwrite the others settings.
I have been thinking that I should get rid of the windows registry anyway to make the code more portable. A setting file in the LCDInfo directory would probably be a good choice. This would also allow configuring two different instances in two different directories.
The source code of LCDInfo is already available so you can do it yourself.
http://forum.lcdinfo.com/viewtopic.php?t=854
Basically you could modify the functions in registry.cpp to save and read the values from a setting file in the LCDInfo directory instead of the windows registry. I'd be glad to see this change made and to put it in future LCDInfo versions.
One instance of LCDInfo can't handle two displays currently but I have had some thoughts for this too and it should be possible to make it happen sometime in future. But I think there are other more important things to do first so the simplest way now would probably be to modify the registry.cpp like I said above.
Hmm now that I think about it there might be some issues with the icon and two instances. But I guess it shouldn't be that difficult to make some modifications to make it work.