This is not 100% helpful a reply, but I have had the Canon 5D Mks II and III and had no issue with triggering flash in live view. I have used both the ST-E2 trigger as well as a flashgun in the hot shoe triggering other flash guns and never a missed shot.
I don't recall any setting that needed to change (in the camera). You need to make the flashgun the master, although that is independent of the live view bit.
Just to pin the issue down - it works when you are not in live view, but no trigger when live view is activated?
Can you try a flashgun in the socket and see if that works?
Steve