I think if anything if that
is Doomtrain, there might be an actual connection with the Lucian ring and the one mentioned in FFVIII depicting the ring being that of a royal line. The rings looks very similar to each other, but I believe there's more to it than just that (if a connection even truly exists).
The ring from FFVIII (referenced previously on Mognet I believe) is from the Occult Fan III where it depicts a ring believed to have "belonged to a royal family" which is quite clearly referencing Seal of Solomon, the famous ring owned by King Solomon. Interestingly, as
explained in the etymology section of the FF Wiki, the ring allows Solomon to control demons at his own will. The demon named Glasya-Labolas is the Japanese name given to Doomtrain which is one of the demons depicted in Goetia.
So, where is the connection here? Well, I believe if Doomtrain does exist, and there's a connection to Lucian line, it could have something to do with the ring. Given that Lucis worships the reapers, and the reapers are depicted as doing the bidding of the four in the center of the Genesis artwork, it's likely that they are able to command these demonic beings through some means. Doomtrain being another example of a demonic creature might imply that the abilities of the ring extend to the ability to control these demonic creatures.
I believe that this might also fall in line with the Shakespearean quote that was referenced back in the early days of Versus XIII, "there is nothing either good or bad, but thinking makes it so". To this, it might suggest that controlling these demons in the eyes of man is a bad thing, perhaps they toy with the idea of death?
Anyways... I think it's very possible for Doomtrain to exist in this game, although, I don't know if this is necessarily Doomtrain. It would be pretty cool if you were able to control demons as Noctis though...