Luthor would have to be Alexa. I can't imagine Claire being both Superwoman and her normal persona and being fooled by a male Lex.
I would invision Claire with glasses and pulled back hair in her normal persona and in the Superwoman persona no glasses and hair down.
Then again... we could have her costume have a mask. Although I'm pretty fond of this costume:
http://www.superman-v.com/images/supergirl%202.jpg It pretty much kicks butt.
