It's a setup for a sequel, so there is not enough information in the movie itself to say for sure, but it's a pretty good bet it'll be Darkseid, since one of Batman's dreams featured Darkseid's Omega symbol and winged beings that look like parademons, Darkseid's flying troops. See this article for some more discussion.
As for how Luthor would know, I can't say for sure, but KutuluMike pointed out in a comment that Warner Brothers has released this deleted scene of Luthor on a Kryptonian ship, apparently communing with the hologram of a being that seems to be holding some mother boxes (the type of computer used on Darkseid's planet Apokolips, as well as his enemies on New Genesis), some have speculated this being could be one of Darkseid's generals named Steppenwolf, or Darkseid's father Yuga Khan. Hopefully the Justice League movie will explain Luthor's knowledge of the threat in more detail, along with explaining why Batman would be having some kind of precognition of the future when he isn't normally psychic, rather than just treating this stuff as "foreshadowing".
From this page which offers a good rundown on Darkseid, here's a shot from a comic of Darkseid showing off his Omega symbol:
And here's the same symbol burned into the landscape in Batman's dream:
Here are the parademons in the comic:
And some of the flying things in Batman's dream:
A close up showing what looks like glowing red eyes: