First appearing in Superman: Earth One - Vol.2. Doctor Alexandra Luthor, created by J.S. Micheal & Shane Davis, is shown to be just as smart if not smarter than Lex Luthor.
Alexandra and Lex have their own company called "Lex Squared Incorporated", she is a Theoretical Physics who works at a undisclosed university (possibly Metropolis U). She is currently pondering how to alter light frequencies through projected energy, reasons as to why is speculated as having something to do with finding a way to hurt or possibly kill Superman.
Throughout much of Vol.3, we see a very different type of Lex Luthor character. He's more interested in knowledge and genuinely interested in whats best for Mankind, his interest in Superman on Earth One is purely about how they can better the people of Earth. Alexandra however is much played out with a much crueler manner, echoing many versions of the the Lex Luthor many of us have come to know throughout the years. The only thing she truly cares for, or at least appears to care for, is her husband.
Towards the climax of the 3rd volume, Lex is critically injured by Zod-El. As he appears to succumb to his wounds, it is revealed that he is actually alive via stasis chamber. Alexandra vows to both find a way to heal her husband as well as kill Superman for his involvement in Lex's injuries (even though she is actually directly responsible for it), she states that she is to no longer be referred to as "Alexandra", but as "LEX"! This effectively makes her Superman's arch enemy in the Earth One series.