As far as I can understand of the stories, Nitocris Caster is the Lovecraft based one, as the only underworld or magic connection Nitocris had was from Lovecraft using her name as the Queen of the Ghouls. The Summer Assassin is actually the history based one, as her legend as making an underground room that could flood as revenge for her brother's murder. This new Nitocris is just the Caster gone Super Saiyan or something similar.
Its not often that the swimsuit version of a servant more accurately reflects their historical origins, but that is the case with Nitocris.
Well, I'm surprised. Never thought I'd see the day when Nitocris gets an Alter version. I don't follow what's going on in JP anymore, but I wouldn't be surprised if this version of her became an SSR. By the way, as far as I know, she is the second FGO original Servant (meaning one that hasn't been seen in any other form of Fate/-media before their FGO-release, in case that wasn't clear) to receive an Alter version. The first one being Arjuna.
Edit: Also excluding NPC like Marie Alter and basically every Arturia-clone (namely Lancer Alter and MHX Alter), because in the end they're still Arturia.