No, I don't think Voldemort would give up easily, but I'm not sure how smart Voldemort is either. Maniacal villains tend to have a lot of blind spots.

Lucius seems too calculating to just be a blind follower. I don't know if he is necessarily smart but he knows how to play the political game. It'll be interesting to see what happens to him in the next two books no that he is in prison and his family name in ruins. I really doubt he is going to stay in prison long whether he is freed or he escapes.