She was beautiful and she was in love with him.

Lucius had been fairly amused when his son had come home for his first Christmas from school and told him that one of his classmates had a schoolgirl crush on him.
He had been decidedly less amused when, during the brief period he had gotten rid of Dumbledore, she had told him in no uncertain terms that "this is no childish infatuation, this is serious! Don't give me that look, I do know the difference". That was one of the few things that endeared her to him; she was a pureblooded girl who fought back. There really were not many of those and he savoured it, but she was merely a friend of his son's who had latched onto him for the blossoming of womanish feelings. Well, she had been until he had ran into her today.

"Lucius," she sighed, come out of the tea shop behind him and interrupting his reverie. "One night."

"Excuse me?" he said, icily, rotating a hundred and eighty degrees to face her.

"Give me one night of love and then I'll walk away forever." She would not beg, no more than he would; they both knew that the world owed them even their slightest whim.

He nodded curtly. "Where did you have in mind?" He did not want to be seen going into her home any more than he wanted to take her back to the Manor.

"There's a hotel near here that I use when I'm sick of being watched." He nodded again and the pair stalked off, side by side but not touching, to the Leaky Cauldron.

Break

We can but speculate what happened that night. However, whatever it was, it was evidently successful as, to the great surprise of the young auror on duty, Lucius Malfoy was seen entering her flat the week after at the same hour.

The month after that, she was noted as entering the Manor park at 18:03.

A year later, the pair were married and Draco was sauntering around the ministry boasting of how his 'parents' were the two most powerful and influential people in the world.
Draco never really changed, but then nor did either of them.