Why did the king think the princess's lover would be disposed of regardless of the door he chose in "The Lady or the Tiger"?

With either door, the youth could no longer be with the princess.

The king’s system of justice includes two doors, which consists of the entire judicial process.  If the accused chooses one door where a lady comes out, he is considered innocent.  He is rewarded with the lady, and there is a marriage on the spot. 

If the accused chooses the door with the tiger, it is assumed that Fate convicted him and he must...

With either door, the youth could no longer be with the princess.

The king’s system of justice includes two doors, which consists of the entire judicial process.  If the accused chooses one door where a lady comes out, he is considered innocent.  He is rewarded with the lady, and there is a marriage on the spot. 

If the accused chooses the door with the tiger, it is assumed that Fate convicted him and he must be guilty. He is mauled by the tiger, and that is the end of him.  The audience watches a gruesome death instead of a wedding.

The king never expected to be so personally involved in the trial. Unfortunately, his daughter, who was also semi-barbaric, fell in love with a man he did not approve of.  There was only one thing to do.

Never before had such a case occurred; never before had a subject dared to love the daughter of the king. In after years such things became commonplace enough, but then they were in no slight degree novel and startling.

The accused will go into the arena with the two doors, just like anyone else.  If he chooses the tiger’s door, he is killed and that is that.  If he chooses the lady’s door, he will get married.  Either way, he will no longer be a problem for the king.

No matter how the affair turned out, the youth would be disposed of, and the king would take an aesthetic pleasure in watching the course of events, which would determine whether or not the young man had done wrong in allowing himself to love the princess.

The king considers the youth disposed of because even if he chooses the lady and lives, his daughter will be through with him.  He will marry the lady whom the king considers perfect for him. 

The princess was invested enough to find out which door was which.  Although we do not know which door she pointed to, we know that her semi-barbaric qualities may have influenced the choice.  She may just have decided that if she couldn’t have him, no one could.