The entire story is that LaCroix gives the PC progressively more absurd quests with the intention of getting rid of him. PC's rise from a fledgling to a power in his own right doesn't sit well with him. He's noveau riche, and wants to pull up the ladder behind him, much like Cicero.
I never quite felt LaCroix was presented in a manner that made sense. Your description is correct, as far as I can tell, but at the same time he's supposed to have been an officer in Napoleon's army - which makes him fairly old, from the Old World and should have seen a lot of things during his time. He should be very skilled in intrigue and information, having risen to the position he's in, and having lived since the XVIII century.
He also should not speak with an
English accent and he should know how to pronounce his own name.
IMO, he's presented like a New Worlder with little knowledge about the Old World. He comes off as insecure like he's just half a century old and comes off as insecure and fairly clueless about how things work.
As much as I would love to praise VtmB in all respects, and I do love the character of LaCroix, he really doesn't make much
sense as a character.