Why did they conspire against him?
'Rashi': They were upset that their relatives died because Amatzyah decided to fight Yisrael.
When did they conspire against him?
'Rashi': It was after they fell to Melech Yisrael.
Refer to Melachim II, 14:19:1:1-3.
Why did he flee to Lachish?
'Rashi': It was a fortified city. Sancheriv fought against it.
Refer to Melachim II, 14:19:2:1.
'Rashi' writes that they killed him 15 years after he fled. Who ran the country during this time?!
'Rashi': Yechalyah, the mother of Uziyah, reigned then. 1
Rashi citing Rabbeinu Yosef, Rashi (Melachim II, 14:19): His son Uziyah reigned then 2 .
'Rashi' calls this difficult. He brings another Perush, and explicitly challenges it (refer to 25:27:4:2 and the note there).
'Rashi': How can this be? After Amatzyah died, they made Uziyah king, when he was 16. When his father fled he was only one year old! Also, if they made him king in his father's lifetime, it should have said 'b'Chayav'! Radak (Melachim II, 14:19) - also, it says (14:2) that Amatzyah reigned 29 years [in Yerushalayim - PF]! According to this, it was only 14! (Hiding in Lachish is not ruling in Yerushalayim! - PF) Also, the verse says that his son ruled only 52 years, and they were after his father's death. (Perhaps the verse (15:1) includes the years he ruled in his father's lifetime! - PF) If you will count the 15 years for his son, he ruled 67 years! Also, "va'Yanas Lachishah va'Yishlechu Acharav" implies immediately after he fled!
