Oh, Lavinia. She isn't imaginative or interesting or anything that might make her appealing—she's just mean. Like, Mean Girls mean. Check out what she says about Ermengarde: "She IS too fat," said Lavinia. "And Sara is too thin" (6.10).
Seriously, could you get any more typical than that?
Lavinia immediately hates Sara because she threatens her Queen Bee status. She's jealous of Sara's nice clothes; spiteful and when Sara's father dies; and probably has only hateful things to say once Sara regains the diamond mines. Good riddance, Lavinia.