To whose life does this refer?
Radak: Chazal (in Yalkut Shimoni 252) disagreed. Some say that it is Yehoyachin's life, and some say that it is Evil Merodach's. Presumably, it is Yehoyachin's for when Hashem gives serenity to Tzadikim 1 , He does not take it from them. Rather, it goes with them to Gan Eden.
Yehoyachin "did evil in Hashem's eyes, like all that his father did" (24:9)! However, a verse (24:19) says similarly about Tzidkiyah, who was a Tzadik (Sanhedrin 103a)! (PF) Both of them repented in exile (Shir ha'Shirim Rabah 7:1). Radak (Yirmeyah 22:24) - Yechanyah repented in jail. Rashi (Chabakuk 2:4) - he was a Tzadik. Rosh (Midos, Sof Perek 2) - he entered the Mikdash to take Reshus before going to exile. Rav Elyashiv (Teshuvos 4:267) - he merited that a gate of the Mikdash be named for him, for he departed from it after his friends and relatives, which shows that it was dearest to him.