We never see the prime universe Lorca.
Lorca is introduced in "Context is for Kings" (episode 3). At this point, he's already light-sensitive. His first line is:
LORCA: Forgive the lighting, or lack thereof. Recent battle injury. There's nothing they can do if I wanna keep my own eyes, and I do.
At the end of "Vaulting Ambition" (episode 12), Michael and Georgiou have this conversation:
MICHAEL: You're sensitive to light.
GEORGIOU: Only compared to a human from your universe. It's the singular biological difference between our two races.
and then Michael realizes that the Lorca she knows is the mirror universe version.
Since he's always been light-sensitive, he must have always been from the mirror universe.
Moreover, when he's talking to Michael in "What's Past is Prologue" (episode 13), he explicitly says:
LORCA: I see you, Michael Burnham. I see your power. And I'm offering you a future. I have since the day I brought you onto the Discovery.
which only makes sense if he's been in command all along.