Why did the Princess hate the Lady?
The princess hates the lady out of pure jealousy. The lady is described as "one of the fairest and loveliest of the damsels of the court." The princess has seen her looking at her lover and has caught them talking together. These facts or fancies may not have been sufficient to make an ordinary woman insanely jealous, but the princess has inherited her father's savage temperament, and she hates the other woman
...with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors...
If it were not for the passionate and barbaric temperament of the princess, the reader would have no touble deciding whether to direct her lover to the door concealing the beautiful rival for his affections and not the door concealing the ferocious tiger. His fate hinges entirely on the emotions of the princess. Does she love him enough to want to save his life? Or does she love him so much that she would rather see him torn to bits than give her to another woman, especially to a woman she hates?