Earlier, in verse 7, Mormon made sure to note that the king of the Lamanites was at the head of his army. That information leads directly to this episode where the king is among the injured. In later Maya descriptions, the kings are often depicted as warriors, and while some of them were more likely only symbolically present, it would not have been surprising to find a king on the battlefield. Note that later in the book of Alma we will have Alma himself in battle.
That the king was wounded, but not dead, is also part of ancient warfare. The types of injuries that would debilitate occurred frequently, and the actual dead were often fewer than the injured. In this case it is fortuitous, and perhaps divinely fortuitous, that he is alive, even though injured.
The people of Limhi suggest that Limhi kill the king. Although they could have done so on the battlefield, it was more appropriate for their king to pass judgment on another king. Therefore, while they suggest that Limhi kill him, they nevertheless allow Limhi to make his own declaration of the Lamanite king’s fate.