"Cissy" (as Bella likes to call her) and her husband are having kind of a rough time these days. Voldemort has taken over their house, and they seem to be in something other than the best standing with the Dark Lord.
Voldemort seems to enjoy taunting Lucius at one point, suspicious that his "loyal servant" is not actually that eager to offer up his wand when Voldemort explains he needs it to kill Harry:
VOLDEMORT: […] I face an unfortunate complication: that my wand and Potter's share the same core. They are, in some ways, twins. We can wound but not fatally harm one another. If I am to kill him, I must do it with another's wand. Come, surely one of you would like the honor, hmm? What about you, Lucius?
LUCIUS: My lord?
VOLDEMORT: [imitating Lucius] My lord? I require your wand. [Lucius reluctantly gives it to him.] Do I detect elm?
LUCIUS: Yes, my lord.
[Voldemort breaks the wand.]
Later, when the Malfoys and other Death Eaters believe that they might have Harry Potter in custody, Lucius is elated because he's convinced that if Draco can confirm Harry's identity and the Dark Lord comes, all the Malfoys will be forgiven for whatever failings in loyalty/commitment the Dark Lord has accused them of.
Unfortunately for old Lucius, Draco isn't playing ball. Remember how Draco basically refused to step over the line into murdering people in the last film? Anyway, he's still not into Death Eater ways, and he really seems to resist identifying Harry concretely.
Sure, it might just be that he really doesn't want Voldemort to show up, but we're taking a more charitable view: We think he really just doesn't want to be responsible for Harry's death, no matter how much they hate each other. We said it in the last film, but it's worth repeating: Maybe this Malfoy kid really isn't all bad.