I think unless they're competitive like Ed, Rose, Dara, James, etc, they would prefer to show up less prepared for more comedic effect. Also to be fair, Katherine bashed out several random miracles in a small space of time, I barely remember it myself, as a die hard TM fan.
Lucy is a weird one. That gang task suggests she has absolutely no reading comprehension. She seems to be meandering her way through the show just doing whatever she feels like, and never knows what's happening. Even in the studio she doesn't seem to be that aware of the fact that she did something completely different to everyone else.
I don't understand how she can be so unaware. I can't think of a previous contestant who was like this.