It wouldn't make much sense, though. Draco had no shame. He always felt himself guilty of nothing, was embarrassed by the same. There was not much sense in hiding his family's unsavory past to anyone, much less his son. She didn't know how she felt about him telling these things to Lucio, either. If he wasn't careful, Lucio might grow up to idolize and try to emulate or even follow the same path as them.