I've been experimenting with live view on the 5Dii and for some reason it wouldn't let me select the ISO manually while I was in Aperture Priority mode.
There was some evidence on the internet that this wasn't possible if you had your live view settings set to Stills+movie. That didn't make me happy because I still want to retain the ability to shoot video quickly if I want it. But actually I figured out that you can have your Stills+movie cake and eat it too.
To do it, on the second screen for LV func. setting, just be sure to select either "Stills display" or "Exposure simulation" and you'll be able to change the ISO manually while in live view/Aperture Priority by pressing the ISO button. (But if you have the second display set to "Movie display" it will only let you use Auto ISO.)
I find that using the Exposure simulation setting is pretty useful. If, while in live view, you hit the Info button a couple times, it will show you an RGB histogram. This makes for a pretty nice way to determine a good exposure, I just spin the rear control dial (with the power switch in the highest setting of course), until the histogram is where I want it (usually exposing to the right until just before one of the channels clips).
I find that I don't miss "Movie display" at all because as soon as I start recording video, the 16:9 crop lines still show up. I just don't get them before I hit the record button. I guess this could be bad if you're carefully setting up a video and need the crop lines for framing, but with quick handheld videos like what I do most of the time, it's not an issue. And if you're carefully doing video, you'll have your settings set for Movie display anyway.
Note: my camera is on firmware v2.0.9 if it matters.