So I remember investigating a few things with this menu bar at one time. My goal was to just remove the menu bar all together, without using VI Server. If your window implements the menu bar using some kind of standard Windows menu bar then this is relatively trivial, and using the GetMenu on user32.dll returns a reference to the menu, and SetMenu sets the menu.
The problem I've found is that LabVIEW implements menus not as a standard menu bar, and using this Get and Set don't work as expected. I show an example of how to insert notepad in a front panel window here, and I can remove and add the menu bar using this DLL calls. (here is the post with source)
My point in all of this is, if you found a way to change the color of a LabVIEW menu bar using OS calls, I'd be very interested in it. In my investigations I couldn't find a way to easily remove the LabVIEW menubar, let alone change any of its properties.
Oh and the color probably comes from the theme applied in Windows, so if you are able to change all menu bar colors then that could be tried.