I'm not sure we ever will. Presumably, [our] Lorca was transported to Mirror Lorca's ship moments before it was destroyed, and likely killed in said explosion. Mirror Lorca was using the transporter, and we know there's always a switch in place, so as far as I'm concerned (or as far as we should be I guess), our Lorca is long dead.
Well, you obviously know what happened to him in the Kelvin Universe. In this universe though (the prime universe) he's involved in an accident that severely cripples him (there's a TOS episode about it); he goes on a mission with Kirk and Spock to an alien world where he's restored, but he must remain on said world with a woman he knows (or knew) and the aliens that inhabit the planet. My memory of the episode is a little vague, but this is ultimately what'll happen with him.
Whilst I'll agree that she isn't the most inspiring character, I don't feel the show is truly about her. Short of the first couple of episodes, it's felt like an ensemble crew to me.