If you set the aperture before turning on LiveView you will be at the preset aperture. I assume you are using aperture priority mode.
I have taken hundreds of moon photos but I don't think ever in LiveView mode. I always see lots of detail but never use a lens shorter than 400mm. If the lens has VR I also handhold. Here's a recent moon shot taken with the D800, AFS 300mm f4 and the TC 20E III, wide open.