At least four, and possibly up to nineteen (depending on whether or not they were all in on the entire plan) chose to die for a lie on 9/11. So much for that argument.
Your argument's been raised already, and answered. You might die for a lie that you believe, but if you are yourself the liar, almost certainly you won't. There might be situations it could happen ("The judge said, 'Son, what is you alibi? If you were somewhere else then you won't have to die.' I said not a word, though it meant my life, for I had been in the arms of my best friend's wife." Long Black Veil, Dave Matthews Band) but not with so many people.
So much for that.