The lockdown could've been an effort to impede the Bureau agents from interfering.
The only way killing Trench makes sense to me is if he wasn't good enough for the Hiss.
The Hiss had control over Trench and the Slide Projector was active, so shouldn't they have been able to attack the Board right then and there? Maybe they needed a stronger parautilitarian to force themselves through to the Astral Plane?
If that's the case, then replacing Trench with Dylan would make sense. And it would make sense that they were able to attack the Board after possessing Jesse momentarily.
Hmm, interfering how? And interfere with what? We're repeatedly shown that the control agents are basically powerless. All the named officers/executives either get corrupted by the Hiss or are ineffective on their own. Jesse says (multiple times I think) that if the Hiss get outside then it's over. The lockdown actively prevents the Hiss from escaping. It doesn't appear that there's a limit to the number of people the Hiss can posses, so I don't think there would be a reason they couldn't control *both* Trench and Dylan. In other words, Trench wouldn't have needed to be replaced. I was down with the idea that possessing Jesse was what got them an "in" with the board, but if that was the case, they should have been able to do that with Trench since he also had a connection with the board as the previous director.
I don't really have any solid ideas about the lockdown. Does it explicitly say that the Director enabled it? I only thing I recall is that they can disable it. Its possible the Oldest House has its own security protocols in place to put itself in lockdown for emergencies.
I thought there was an audio log from Trench that said he wanted to be the single point of failure. In any case, since the Director can disable it, Trench could have just lifted it even if the Oldest House automatically put some protection in place. Along those same lines, since none of the npcs you talk to have any hint that Trench was being controlled by the Hiss a live director would still have been able to do more for the Hiss than a dead one. In fact, in what I'm sure is intentional misdirection for the player, the npcs suspect Dr. Darling of being up to something more than Trench.
I'm actually kind of hoping that I missed something important, but since it's not obvious it seems like it might just be a plot hole/questionable twist to make the guy you were sort of trusting into the bad guy. I don't think there was a "what have I done" moment for Trench which might (?) have explained it.