There was a reason, though, that Ahaziah wanted Elijah to come down from his hill. He wanted to ask Elijah to ask God if he was going to recover from his illness. And now that the third group of 51 got Elijah to come down from his hill, Ahaziah could ask Elijah to ask God about it.
[But Elijah had already told Ahaziah (via messengers) back in 2 Kings 1.6 that God was going to kill him for asking the wrong god, so I don't know why he had to send the three sets of 51 to asked Elijah again. I guess he wanted Elijah to come down and give him the message directly.]
In any case, Elijah came down the mountain to talk to the king.
He arose, and went down with him unto the king. 2 Kings 1.15Here's what Elijah told the king (again).
Thus saith the LORD, Forasmuch as thou hast sent messengers to enquire of Baalzebub the god of Ekron, is it not because there is no God in Israel to enquire of his word? therefore thou shalt not come down off that bed on which thou art gone up, but shalt surely die. 1.16And in the next verse, king Ahaziah dies "according to the word of the Lord."
So he died according to the word of the LORD which Elijah had spoken. 1.17God's next killing: two bears rip apart 42 boys for making fun of a prophet’s bald head