Yep, Lulu has a special Weapon. But you have to do lots to get it. I recommend you to read a walkthrough about ultimate weapons in FFX.
The only thing I know now is that you have to dodge the lightning on the Thunder Plains 200 times. So.. haha, have fun, I never tried it, actually, it's really really hard!
(Btw. the weapon is called Onion Knight ^^)