The wisdom of allowing the king to live is demonstrated when Limhi is able to ask for an explanation. The important subtext behind the exchange is the importance of oaths. The people of Limhi and the people of the Lamanite king had made mutual oaths to each other. Limhi declares that his people have kept their oath, and asks what could have caused the Lamanite king to break his.
The answer is that the Lamanite king saw the kidnapping of the daughters as a violation of Limhi’s oath, and therefore he was retaliating. Limhi appears to see that as a violation of the oath as well, but not one that he had authorized. Thus, he declares that he has kept the oath and searches for those who had not.