I know how much people would love to see Vampire translated to the LCG format, but you likely never will just because of the stranglehold White Wolf has on the entire franchise. They don't play well with other companies, and likely the intellectual property will only become accessible to FFG if White Wolf is cut loose from the EvE Online guys and they need a new company to buy them out.
Likely if you're ever going to see a new LCG from Fantasy Flight that will have multiplayer conflict, it's going to be with one of their in-house properties, the license they have for Warhammer 40k, or something they can acquire through their relationship with Wizards. So where would that leave us?
Fireborn - Not likely as an LCG in my opinion, as the setting and story focus is not on factions or defined conflicts. Would like to see this property see some new life, however.
Grimm (not the same as the NBC show) - Could actually be really interesting, as this one-book RPG does a good job of showing a world with different kingdoms and the re-imagined fairytale concept is trending nicely right now. Also the twisted fairytales vs. children concept could make for a very unique visual style and identity.
Twilight Imperium - This is what I think is most likely for what you would be wanting. They just made the Rex board game, have shown they have a real dedication to the setting, and there's the old RPG material and collectable tactics game from wayyyyy back in the day for inspirations. It also has defined factions that would convert really nicely into strategy styles and deck formats, as well as an established setting where alliances can happen. I would see it as some sort of "Location Control" mechanic that's present in a lot of the existing games, as well as down and dirty fighting.
Tannhauser - Alternate History Deiselpunk vs. Magic. What's not to love? Likely would max out at 4 players battle royale.
I'm sure there are other possibilities, but that's what I can think of right now.