Sara Crewe is most definitely the hero (or heroine) of her own story. You might expect a little girl who's been raised in riches and comfort to collapse in despair when thrust into dire circumstances, but you'd be wrong. Sara rises majestically (har har) to the challenge.
And that's one of the reasons Miss Minchin hates her so much. Even though Sara is polite and dutiful, she won't lie to appease her. She stays strong and true to her good upbringing and continues to act like a princess... and is rewarded by the end with great riches.
Lavinia may be annoying, but the true bad guy in this book is Miss Minchin, the headmistress of the boarding school. Here is a woman who has very little sympathy for anyone—from slow Ermengarde to motherless Lottie. And the person she has the least sympathy for is Sara, who is newly orphaned and doesn't have a penny to her name (supposedly). Instead of treating her with compassion, Miss Minchin revels in making Sara's life harder by depriving her of meals and mocking her for thinking that she's a princess.
In the end, she gets her comeuppance when she discovers that Sara really is rich, and that she's going to miss out on all that money because she was super mean to her. Serves her right!