At Hailsham, Miss Lucy is the newbie and the rebel. She's recently been hired as a Hailsham guardian when Kathy and her friends are students. Let's put it this way: she definitely brings some excitement to the Hailsham party. She's not about to go with the flow.
Here's the thing about Miss Lucy: any time she shows up in a scene, you just know you're going to get some juicy information. Granted, each time she'll only let a few tasty details slip, but we'll take what we can get. You see, Miss Lucy is like the Anti-Miss Emily. While Miss Emily wants to control all the information, Miss Lucy makes it her mission at Hailsham to clue the clones into the reality of their situation. She's going to tell the students the truth about their future or get fired trying.
And that's exactly what happens. Sadly for all the honesty-lovers out there, Miss Emily makes it clear that Miss Lucy's antics (you know, telling the truth) will not be tolerated at Hailsham. So she gets the boot. But even though she's only at Hailsham for a little while, Miss Lucy definitely has a big impact on Kathy and an even bigger impact on Tommy.