God sent a Prophet from Judah to Bethel to proclaim a message from the Lord to the Jeroboam, and then not fellowship with anyone, but to go back home. Later, an old (second) prophet came to the first prophet, and lied to him. He said:
And he said to him, “I also am a prophet as you are, and an angel spoke to me by the word of the LORD, saying, ‘Bring him back with you into your house that he may eat bread and drink water.'” (1Ki 13:18)
So the first prophet went off with the second prophet, and ate with him. Then things get weird:
And as they sat at the table, the word of the LORD came to the (second) prophet who had brought him back. And he cried to the man of God (first prophet) who came from Judah, “Thus says the LORD, ‘Because you have disobeyed the word of the LORD and have not kept the command that the LORD your God commanded you, but have come back and have eaten bread and drunk water in the place of which he said to you, “Eat no bread and drink no water,” your body shall not come to the tomb of your fathers.'” (1Ki 13:20-22)
Sure enough, on the way home, the first prophet died. The second prophet hears about it, and then:
And he (second prophet) went and found his (first prophet) body thrown in the road, and the donkey and the lion standing beside the body. The lion had not eaten the body or torn the donkey. And the prophet took up the body of the man of God and laid it on the donkey and brought it back to the city to mourn and to bury him. And he laid the body in his own grave. And they mourned over him, saying, “Alas, my brother!” And after he had buried him, he said to his sons, “When I die, bury me in the grave in which the man of God is buried; lay my bones beside his bones. (1 Ki 13:28-31)
So, why didn’t the lying prophet get killed too?
We’re not told. Lying in the name of God as a prophet was a pretty serious offence. Though it wasn’t actually false prophecy, just a straight out lie. Maybe the second prophet worried about his standing before God, and this explains his action? But we’re not told. (Just like we don’t know why God didn’t kill Judah)