The past events in Hexed are similar to Fall of Cthulhu, as Lucifer starts the series with the "H" tattoo on her back that she received at the end of Fall of Cthulhu, and she mentions having been involved in a "turf war" in Massachusetts (where the town of Arkham is located). She may also have encountered Hexed versions of characters like Cy Morgan and Sheriff Dirk. However, the Godwar in the Hexed-verse was a conflict that involved generic demons and other supernatural beings, rather than the gods of the Cthulhu Mythos.
Likewise, in the universe of Fall of Cthulhu, Lucifer's life post-Godwar was similar to the events in Hexed, with her encountering the Fall of Cthulhu versions of characters such as Val Brisendine, Dietrich and Raina. However, with the presence of the Cthulhu Mythos and its cosmic horror, these events were considerably darker and grimmer than their Hexed counterpart, with Lucifer getting involved in a conflict with beings like Yog-Sothoth and Shub-Niggurath, their cultists and non-human races such as Ghouls and Mi-Go. Even Nyarlathotep may have returned to plague her. Consequently, by the end of the Mythos version of Hexed, Lucifer has been further traumatized and is still burdened by her tattoo, and the Harlot is still very much alive.