Draco's daddy is about as warm and cuddly as the younger Malfoy. Like Draco, he's snobby and haughty, and he's definitely sympathetic to the Dark Lord.
One of the big cornerstones of Voldemort's whole movement was playing up the supremacy of wizards—and especially pureblood wizards—over Muggles (non-wizards) and half-bloods. You know, sorting out the "elites" from everyone else.
Lucius seems to adopt that superior attitude in dealing with lots of folks—like the Weasleys, for example. When Lucius and Draco run into Ron and his family at the Quidditch World Cup, Lucius makes it clear that he thinks he's well above the Weasleys in status:
DRACO: Father and l are in the minister's box, by personal invitation of Cornelius Fudge himself.
LUCIUS: Don't boast, Draco. There's no need with these people.
When Voldemort returns, though, Lucius finds himself in a little bit of hot water. See, he never really made that much of an effort to find out whether Voldemort had survived his encounter with Harry thirteen years ago, and Voldemort is not pleased:
VOLDEMORT: […] I confess myself disappointed. Not one of you tried to find me. Crabbe! Macnair! Goyle! Not even you, Lucius.
LUCIUS MALFOY: My Lord, had I detected any sign, a whisper of your whereabouts…
VOLDEMORT: There were signs, my slippery friend. And more than whispers.
Slippery is right. Lucius wants to have it both ways, it seems: he's a follower of the Dark Lord, but somehow he's managed to stay out of Azkaban by keeping his sympathies on the down low.