Solas told her because he thought she needed to know the truth, not caring of her thoughts, her ideas, her feelings on the matter. Lavellan won't tell because she knows that some truths are best buried, hidden and hiding. She's kinder than he is.

"The Dalish are a people but they aren't. It can shift and change, flowing forms. You could feel a different Dalish. After all, you still care."

Lavellan was still Dalish. She might not believe in the gods, the culture might be different, but she still cares about her clan, about their feelings, about their hurts. That could still make her Dalish.