Affiliation: Death Eater
We don't see much of Lucius Malfoy directly in Goblet of Fire. We know that he has a lot of influence over the Ministry of Magic, and especially over Cornelius Fudge. When Harry tells Fudge that he saw Lucius Malfoy with the resurrected Voldemort, Fudge protests weakly, "A very old family – donations to excellent causes –" (36.128). But no matter how blind Fudge may be to Lucius Malfoy's real loyalties, it's pretty obvious to everybody else.
After all, Voldemort addresses Lucius directly as his "slippery friend" (33.54) when he's brought back to life. Voldemort compliments Lucius:
I am told that you have not renounced the old ways, though to the world you present a respectable face. You are still ready to take the lead in a spot of Muggle-torture? (33.54).
Clearly, Lucius is a Death Eater through and through, and Draco supports his father's affiliations.