The laptop is more than powerfull enough, The RAM is plenty.
With that sort of set up I would be surprised if the video card was not up to the job, You indicate that the trial runs were OK so the live lecture should not be a problem - The number of screens you show the lecture on is not an issue - The signal just goes through the video cable and that's it!
All I can think of is that there is something else running on the laptop - Anti-virus software perhaps? That keeps checking the video file, Possibly ever time a frame is displayed.
That would certainly cause the problem you are seeing.
If possible, Shut down everything you have in the system tray (Even Anti-virus software, Just temporarily) and see if it helps.
If it does re-introduce the applications one at a time and then re-test. This will pinpoint the exact moment a problem occurs.
Hope that helps.
Gary.