Too much negative attention.

 

She gets attention by behaving badly. Parents give her attention to alleviate their own anxiety about her. She knows which buttons to push to get that attention. Negative attention is still attention. A cycle forms.

Remind her to love herself more ("We love you as parents, but you need to love your self. Telling lies means that you don't see yourself in the right light.") and learn to take responsibility for her own words and deeds. Feeling is OK but thoughts should follow, quickly. Ask "Why do I feel this way?" Become more self-aware, a measure of maturity. Don't feel like to be mature? You pay a price sooner or later.

You mentioned Bible verses. There're children's versions that fit her reading level. Food for thought.

There should be a balance in the attentions paid to the brother and her. Prais her more.