Might be reading a bit too far, but Lyog shaping up to be quite competent here.
He properly remembers a random bounty out of who knows how many and he seems to got his priority in order, although subscinsciously. Like, of course he gonna prioritize catching a bounty that actually threatens citizen's life instead of a search demand from some noble that he doesn't even know the reason of. For all he knows, the noble might be just flexing his authority and shit.