Lena doesn't remember the first time she learned that being a Luthor meant being a villain. Maybe it was when she saw her brother, dear Lexie Luthor, strangling Superman with Kryptonie gloves on national television. But that can't be right, because she remembers even before. The rumors that Lex had caused the earthquake that killed so many people, or how he had allowed miners in some country to die, in order to frame Superman. She had defended him so many times, just to have her heart ripped apart when she found out it was true.
And when she asked him why he did it, he just snarled "To protect us from the aliens." She saw perfect sincerity in his eyes, and realized he believed what he was saying.
She nearly slapped him right there. Lex could lie to the world, maybe to himself, but he couldn't lie to a fellow Luthor. He had practically raised her, had taught her how to be cruel, how to know when to lie to an enemy, when to pull punches to push the enemy into a false sense of security. So she knew, by then, how to look past any of his lies. It was easy, after she learned to look past the lie that he actually gave a damn about her.
But now, she is left with a legacy. A legacy of hate, of evil, of generally being a jerk. And everyone she meets knows it. They expect it of her. Even Supergirl has it in her eyes. A certain distrust, a distaste that colours every interaction.
But Lex once told her "Luthors make their own destiny."
And Lena is a Luthor. And she intends to be the best Luthor of all, even if her brother would never see it that way.