^Dante gave the Sparda?!? Wasn't it Trish who took it to them just to 'lure' Dante into Fortuna Castle to do some demon butt kicking?
I believe it is like this:
Lady turns to Dante and asks for help to kick down some demon-worshipping cult. To be sure how they work, Dante asks Trish to go undercover by turning herself into the form of Gloria and hands over the sword Sparda to gain their trust faster. She has then discovered some things which she reported back to Dante who then crashed down the ceiling of their church and headshotted their leader.