I don't completely understand God's thinking on this one. Maybe a believer can explain it.
It all happens fast, in just two verses. Here's a summary:
A "son of a prophet" asked a "neighbor in the word of the Lord" to smite him.
A certain man of the sons of the prophets said unto his neighbour in the word of the LORD, Smite me, I pray thee. 1 Kings 20:35a
The neighbor refused.
And the man refused to smite him. 20:35b
So God sent a lion to kill him.
Then said he unto him, Because thou hast not obeyed the voice of the LORD, behold, as soon as thou art departed from me, a lion shall slay thee. And as soon as he was departed from him, a lion found him, and slew him. 20.36
It turns out, though, that there was some reason to the prophet's madness. The prophet wanted a good disguise when he met King Ahab, and he figured a wound would help. So he wanted his neighbor to cut his face, so he could put a bandage on it, so King Ahab wouldn't recognize him when he saw him. Or something like that.
(I don't know why the prophet couldn't just put a bandage on his face or a bag over his head to disguise himself. And I'm not sure why the disguise was necessary anyway. But I guess it was all very important to God.)
Anyway, the bat-shit crazy prophet found another guy who was willing to smite him.
Then he found another man, and said, Smite me, I pray thee. And the man smote him, so that in smiting he wounded him. 20:37
And so the prophet got his costume ready for his meeting with King Ahab.
So the prophet departed, and waited for the king by the way, and disguised himself with ashes upon his face. 20:38
Which leads us to God's next killing.