Lydia is one of Lucifer's many daughters, but she's more interested in playing with her hellhounds than she is in starting wars or famines or anything like that. In short, her father views her as a colossal disappointment.
Her siblings do, too, teasing her constantly.
But Lydia knows who she is. She is the daughter of flames, and she will be who she wants to be.
Not her brothers.
Not her sisters.
And most definitely not her father.