逝かせて comes from 逝く, a poetic and respectful way to say “to pass away,” rather than the everyday 死ぬ (“to die”). In the song, the narrator imagines a “gentle god of death” allowing him to pass peacefully as long as he is with the person he loves, giving the word a dramatic and tender nuance.
"HEAVEN" is a love song that keeps sneaking death into the room, and somehow it stays sweet. It opens with the singer telling his partner to stop looking so sad and just wait, because he's coming to get her: "迎えに行くから" (I'm coming to pick you up). Then he kicks off from the scorching asphalt and asks, "このまま二人で 天国まで行こうか" (shall we just go, the two of us, all the way to heaven?). It works as a joyride and as something heavier, and the rest of the song leans into both.
The promises are huge. Being born in the same era as her is, he says, the whole reason he's alive, and even if they're reborn he'll find her again "同じ場所で" (in the same place). He wants to be the sun so she never wilts, which pairs nicely with the shy line "愛の言葉はテレるけど" (words of love embarrass me). テレる is the casual way of saying you feel bashful, the blushing kind of awkward. The ending goes darkest: if he could die holding her hand he wouldn't mind, because with her there "優しい死神がきて" (a gentle grim reaper would come) and let him go peacefully. 死神 literally means "death god", and making him gentle is the song's whole trick: as long as she's beside him, even the end doesn't scare him.