TC, that's a really good point. That seems pretty inconsistent. He also kills Bob Barbas's human form through Limbo too, when he shoots through the screen and the bullets travel to the real world. That doesn't make sense that he couldn't help Kat out during the raid.
He killed Bob by having killed his true form in the demon world. They killed Lilith in the human world.
To kill one seems to kill the other. Did you see any bullet wounds on Bob?
He killed his demonic manifestation which in turn killed his human counterpart. Not an inconsistency.
I guess it's best not to over-think something like this, and it's not really worth arguing about. It's just a convenient plot device that served the game when something dramatic needed to happen, and Limbo probably won't even be a thing in the next game after what happens at the end of this one, with the two worlds merging.