Well, I've never heard of a woman named Lex, but whatever. I was saying that no one would write a female Lex Luthor, not that the actual name Lex couldn't be used for a woman (although, again, I've never heard of a woman who goes by Lex, it just seems weird).
"Lexi" is a ubiquitous truncation of the famine variations of Alex-. It is also fairly common for those close to her (siblings, best friends, etc.) to further shorten to just Lex.
Though, what I want to know is, why would no one ever write a female Lex Luthor just because you say so?