Lex is the name used by Superman villian Lex Luthor. According to Smallville TV series, Lex is short for Alexander, and this is most probably a link to Alexander the Great.
In the book 'Jurassic Park' there is a girl called Lex. She also features in the first and second film versions. Probably for this reason, I think of Lex as more of a girls' name.
I find this a good name for both boys and girls, but not as a 'proper' name, as a nickname then yes I love it. Before I never actually thought of it as a nickname for a male, as always I thought it to be short for Alexa and Alexis.