ok, I've said it before, I'm no musical expert and I can't carry a tune in a bucket, however, I would think that you should use the reading to display your Lucy voice, and the singing audition to show you can project and keep to the beat. I would go for whatever song will best display your voice and kill at the reading. Any director worth their salt should be able to make the connection. break a leg :-D

Just a quick chime in from me.  I have always found it to be bad form to sing an audition song from the show you are auditioning for.  Just a tradition around here.  However if you realy have big brass ones, walk in tell them Lucy has arrived and hit them with her song. 

If you want to succeed in this game, it takes 80% attitude & the balance made up with apitude, emperical skills & talent.
Something I always suggest, is before your about to enter, keep a tune in your head that best depicts or suits the character - a regal tune for a Queen & you will become one.
Don't worry about being a diva, just prove by your actions, your not a Drama Queen!

I once directed a show where an actor (I knew him but he was new to the group) had a specific role in mind and asked me before the auditions if I would pre-cast because he had to decide between this and another project. Needless to say I declined, I don't believe in precasting (unless I'm the one being pre-cast of course ;)He then asked if he should dress the part, or if there was anything else I might be looking for in auditions. I told him that "look" is the easiest thing to change and therefore the least of my concerns at an audition and to just come prepared to read. He showed up in full costume complete with darkened hair and gold chains looking like an extra from Barney Miller. I cast him, but I also knew him as a fellow cast member and knew he was not crazy. That could have gone either way. Showing up to an audition completely in character is a risky risky move, that depends completely on who is making the decisions and whether or not they think you're crazy. Besides, would you turn down another good role? You don't want to paint yourself into a corner and end up not getting to do the show at all because they don't think you're interested in anything else.