The narrator says that the princess indulges in "grievous reveries" concerning the possibilities for her lover. She knows that behind one door of her father's barbaric arena, a tiger waits to maul her handsome beloved. She very strongly suspects that behind the other door in the arena waits a beautiful maiden who will be only too glad to marry her lover. The princess will either have to watch her lover be torn to shreds by the tiger or watch his "start of rapturous delight" when he sees his new bride-to-be.
These "reveries" are "grievous" because, to the princess, they are both equally horrible. She does not want to see her lover killed and eaten by a tiger; but she also does not want to see him wed to another woman, a woman for whom the princess already feels such crazed envy. Worse yet, the princess actually knows which of the doors leads to death and which one leads to life (and marriage), and she knows that her lover will look to her to indicate which door he should open. His fate, then, is entirely in her hands, and no matter what she chooses for him, it will make her miserable. Thus, as she considers what to do—which door to tell him to open—her reveries fill her with grief.