The tall baron didn't think this Liam's family history was important after Brunilda vetted this future assistant of his. As long as Liam was a decent sort, he would have no issues dealing with anything that might come up.
If what Artemius Holmes said might be true—and the detective tended to be right in his observations more often than not—it wouldn't be too much of a conflict of interest anyway. Nothing he had to stay his hands at because of politics.
A bastard son was always a gray area.
As for Liam being from Leonois. Artemius was probably referring to the civil unrest during the change of power to the newest Holy Emperor. Not only had Emperor Nero murdered his father and slaughtered all other heirs, but he had also crushed quite a few noble families at the start to consolidate his power and push down the legitimacy of his rule through fear.