Hope you didn't make a big wager on this one. Your friend is correct. A player may lift his pivot foot to pass or shoot or stand there like a stork on his non-pivot foot. It's not a traveling violation until the pivot foot returns to the floor. Otherwise, 99% of the layups you see would be travels. In a layup, a player is dribbling to the basket. He ends his dribble by catching the ball while his right foot is on the ground. The right foot then becomes the pivot foot. But what almost always happens next? He picks up the right foot, steps onto his left foot, then jumps for the shot. That's perfectly legal b/c the right foot (pivot foot) never touched the floor again while he still had possession of the ball.
Also, if you couldn't lift the pivot foot, then you couldn't shoot a jump shot, could you?
Chuck