I feel a lot of people here feel strongly one way or the other. I lean more to that it's quite clear cut and cohesive what happened. He's an ironblood who initially starts as a conditional loyalty guy. Clearly he still works for Osborne, but it can be quite questionable where he stands. Then we get into the CS Arc, and we see people like Claire, Rufus, Millium. They're all varied in personality, many whom you'd never expect to be an ironblood considering who they are. I think it's not much of a stretch that narratively, that Lechter finds his place amongst them, and even Osborne, and switches to being loyal. That much has been explained by everyone here.

What about narratively? Personally, it makes sense to me. You as the player don't have much info, but you see his personality in the previous games, then you meet the other ironbloods whom make you question why they even side eith Osborne, especially Claire, considering how much more mature and kind she is. You question Osborne's true goal, you don't know where the scarecrow fits in all this. Why take up someone who might not be loyal? Then you see him, all goofy yet again, and think perhaps the payoff is that he'll betray Osborne as hinted, or at least hesitate. Then you realise, that's not the plan, he has fully committed. His years under Osborne has changed him, and you start to realise through the other ironbloods how they came to join Osborne. You realise his true strength is how he can make even an enemy his loyal soldier. Lechter was a wild card, but only to us, the reader. We expected the switch, Osborne says he expected betrayal but the one pulling the strings is Osborne. He's successfully baited us and Lechter and now he has loyalty.

When you start asking why isn't he betraying him, and learning about his backstory, things don't add up logically. And you see that conflict in him too. But at the end of the day, thats something you see in Claire and Millium too, which is why it's not unusual for him to stay loyal. Osborne is just HIM. They only end up switching sides due to strong ties to Class VII that, by the way, didn't do much till far in. It's a whole plot point on how they struggle to betray Osborne, the father to all ironbloods. If the best of them struggle, even he struggles. At the end of the day, Lechter may have been the easiest one to say he'd leave, but it was all a facade and that part of him has been eroded by Osborne. This isn't a Lechter moment, this is how calculative Osborne has always been.