The fact that the princess loves the young man is not in question- she obviously does, passionately. What will determine the outcome of this scenario is whether this love is selfish or sacrificial. No matter what her choice, this is going to end badly for the princess: she is going to lose the man she loves. She has tortured herself by imagining the results of both her choices.
There is no good option here; the entire trial is immoral and either way, the princess loses. With the tiger, her loss will be over quickly while if she chooses the lady, her loss will be ongoing, something she'll be forced to relive constantly. In the end, what you decide the princess' choice would have been depends on whether or not you think she would choose to put the preservation of her lover's life before her own self-interest and suffering. So... the lady or the tiger?
* Frank Stockton wrote a follow-up to 'The Lady or the Tiger' called 'The Discourager of Hesitancy'.
* Though 'The Lady or the Tiger' is his best-known story, Stockton had many other successful works, and won a Lewis Carroll Shelf Award for one of them: 'The Griffin and the Minor'.