The most interesting thing is that there are times where you really feel that Lorca is devoted to the war effort. I always look at "Butcher's Knife" and the opening of "Sis Pacem" and think that I was totally convinced of his dedication at that point. Hell, he nearly sacrificed the Discovery to shield the Gagarin.
Did Lorca know at that time if he could get back to the mirror universe? If he is stuck in the prime universe it makes sense for him to be on the winning side. But yeah, you make a good point.
This is why I didn't believe the mirror Lorca theory when it was first suggested on here. However ...
This is a point, he still needed more data from jumps at this point to reach the MU, and was still trying to manipulate circumstances to where he could gather it.
Sadly, the true answer is something else:
Jason Isaac is on record in interviews saying his character was supposed to have a "dark secret" from the beginning - but neither him nor the writers knew what exactly it was (Fuller apparently never told them). They came up with the idea he is from the Mirror Universe pretty much on the spot when they were writing the Mirror Universe episodes. In Fuller's original idea - that would have been something completely different, and the early episodes still indicate that.