More theories. They're all I've got. SPOILERS!

OK, so we take as given that Lorca intentionally brought the Discovery to another universe, for all the reasons laid out here.

1. If Lorca's place of origin is wherever the Discovery just jumped to, why assume it's the same mirror universe we've seen in Star Trek previously? Infinite permutations, the man said. If Lorca has never seemed villainously evil, perhaps it's because he's not from THAT mirror universe, but a different one. One that's less evil, but where the Klingon war has gone very, very badly. Which brings me to the next point.

2. Ever since the whole mirror-universe thing came up, I've been assuming that Lorca gets here accidentally, and that his interest in Discovery is exclusively for its ability to travel between the universes (whether because he wanted to do so, or because he wanted to prevent others from doing so). The fact that, after its last jump, Discovery is surrounded by Klingon wreckage indicates that they're having their own Klingon war over there. If Lorca's sole goal is to get back to his own universe, why does he wait this long? Or is there something else he needs to accomplish first? Like maybe finding a way to break the Klingon cloaking device and bring it back with him? So maybe that's been his mission all along -- that's why he came. That's why he needed this ship, this crew -- and Burnham. Not just for the spore drive, but for their ability to solve this specific problem. 

3. OR.....What if Lorca is NOT from the other universe? When Discovery first arrives, he seems genuinely surprised by the Klingon wreckage and genuinely interested in someone telling him where the hell they are. Maybe he's never been there before. Maybe somehow he has the coordinates, but he truly doesn't know where they'll take him or what he'll find when he gets there. But why? Why is he hell bent on going to this one spot in the multiverse? The single weirdest thing about Lorca's story is that he killed his own crew rather than let them fall into the hands of the Klingons. So what if that's a cover story for what really happened? Maybe all this is about rescuing the crew of the Buran, who aren't dead, but have somehow slipped into another universe. Maybe somehow plotting all those jumps has allowed Lorca to figure out the coordinates where his crew are. He knows that Starfleet will never let him turn all his attention to rescuing them, so he made up a cock-and-bull story as a cover while he pursued this secret agenda, because he refuses to give up on his crew. He's been on a dual mission: Win the war and rescue his crew. THIS IS OFFICIALLY MY NEW FAVORITE THEORY.