The Sybil's Story and Latin Class

I was surprised when we found a reference to the Sybil who wished for immortality but not youth in our readings. This is because I came across a story in Latin class, while practicing for the national Latin exam, that I now realize was based off her story. In this version, there was a goddess who relentlessly asks Jupiter for her human lover to become immortal, but forgets to ask for eternal youth. The man becomes miserable because he wishes he could die. She ends up turning him into an insect so that he can at least be out of his pain. In the version of the story referenced in The Waste Land, the sibyl herself is the one who wishes for immortality and then becomes miserable. I was thinking about if the main messages of the stories remained the same, and I do think that if the altered version were the one being referenced in the poem that it would still work. This is because the altered version of the story ties in with the idea of love leading to one's end. Also, the man lives in sort of perpetual in-between-state; he can't fully live as a human, yet he can't die either.