****. If I love the person and he loves me, and my beloved has been through the worst of the Inquisition beside me, then his betrayal must have a VERY good reason behind it.
First, I'd go after him to get some explanations. Then, I'd demand to know what the hell happened to make him change his mind so abruptly. I mean, he could've done this for a million reasons. He could've been coerced. What if by betraying me, he managed to ransom a relative kidnapped by the servants of the Elder One? Or avoided his home village being razed to the ground by an enemy's army? I don't know.
For a person to stand beside you in something so black and white as an inquisition, where your loyalties are clearly defined, people simply won't wake up one morning and think: This is it. I've had enough of ths crap. I'm switching sides! This is war. It's not like picking a fight with a friend because he likes to use plastic instead of paper bags in the supermarket. Or drink Pepsi instead of Coke. This is some serious ****.
You can be court-martialled for this. You can be sent to prison and rot in there for the rest of your (now) miserable life. You can be hanged. You can be beheaded. You can be forced to commit suicide.There are some motherfreaking consequences for treason during wartimes. So I seriously doubt someone would take the initiative to become involved with the Inquisitor unless he knew firsthand full well where he stood in the war.
The alternative would be for him to be a spy or double agent hellbent on working against you. Then it would be the brig or death penalty if the chance for him to escape were considerable. But in this last case, there were no true love for starters, so screw him and his backstabbing. 
So yes, I'd go after him. But not to kill him. Because for such a drastic change to take place, I'd believe until the last minute, 'till the last second, that he was backed so badly into a wall that he was left with simply no other choice. And then, if I managed to learn the truth somehow, then I'd kill the son of a b.... that put him in this whole mess in the first place.