Lamoni’s father clearly feared for his life and pleaded for it. Ammon used that fear to extract a promise that he would free his brothers from prison in Middoni. That statement tells us that Ammon understood that the overking had influence over other kings in the land. It confirms the picture of the king over lesser kings that we have been drawing.
The king is desperate enough that, rather than only agreeing to free the brothers, he offers an even greater reward; up to half of his kingdom. Rather than ask anything for himself, he removes the threat to Lamoni, and then asks for his brothers’ release.