That's a good slippery question. How can you give good supporting evidence when the story doesn't say explicitly if it is the lady or the tiger is behind the door?
The general answer is, if a work doesn't say straight out, look for clues and build a logical argument about them.
The specific answer is, look clues throughout the story for the character of the person making the choice. For example, this young woman is the daughter of a "semi-barbaric" king, one who made justice into entertainment. The very act of doing so is cruel. Therefore, you could argue, she is likely to choose the tiger. Look at other descriptions of her as well. Would someone with "a soul as fervent and imperious as his own" (meaning the king's) let someone else play with her toy (her lover)? No. She would be too proud. She'd give him to the tiger.
And you'd do the same throughout the story, combing through all the descriptions for signs of her character until you built your case.