Lucius Malfoy appears to petition Cornelius Fudge only minutes before Harry Potter's trial over "underaged use of magic in front of a muggle". This occurs 20 minutes into The Order of the Phoenix. In the movie, we only get a glimpse into their conversation:
Lucius: "..., and I'm confident, Minister, that you'll do the right thing."
Cornelius: "Yes, but we must be careful–"
To which they are interrupted by the passage of Harry and Arthur heading toward Courtroom 10. This is directly before Harry's court case.
In the book, this conversation was quite different, occurring after the case, likely Fudge reporting the facts of the case and its holding. Dumbledore's surprise arrival at the newly-designated time and the admittance of Arabella Figg as witness to the Dementor attack were likely of particular interest to Lucius.
“Well, well, well . . . Patronus Potter,” said Lucius Malfoy coolly.
Lucius Malfoy dared look him in the face; Harry could not believe that he was here, in the Ministry of Magic, or that Cornelius Fudge was talking to him, when Harry had told Fudge mere weeks ago that Malfoy was a Death Eater.
“The Minister was just telling me about your lucky escape, Potter,” drawled Mr. Malfoy. “Quite astonishing, the way you continue to wriggle out of very tight holes. . . . Snakelike, in fact . . .”
Mr. Weasley gripped Harry’s shoulder in warning.
“Yeah,” said Harry, “yeah, I’m good at escaping. . . .”
Lucius Malfoy raised his eyes to Mr. Weasley’s face. “And Arthur Weasley too! What are you doing here, Arthur?”
“I work here,” said Mr. Weasley shortly.
“Not here, surely?” said Mr. Malfoy, raising his eyebrows and glancing toward the door over Mr. Weasley’s shoulder. “I thought you were up on the second floor. . . . Don’t you do something that involves sneaking Muggle artifacts home and bewitching them?”
“No,” said Mr. Weasley curtly, his fingers now biting into Harry’s shoulder.
“What are you doing here, anyway?” Harry asked Lucius.
“I don’t think private matters between myself and the Minister are any concern of yours, Potter,” said Malfoy, smoothing the front of his robes; Harry distinctly heard the gentle clinking of what sounded like a full pocket of gold. “Really, just because you are Dumbledore’s favorite boy, you must not expect the same indulgence from the rest of us. . . . Shall we go up to your office, then, Minister?”
“Certainly,” said Fudge, turning his back on Harry and Mr. Weasley. “This way, Lucius.”
They strode off together, talking in low voices. Mr. Weasley did not let go of Harry’s shoulder until they had disappeared into the lift.
“Why wasn’t he waiting outside Fudge’s office if they’ve got business to do together?” Harry burst out furiously. “What was he doing down here?”
“Trying to sneak down to the courtroom, if you ask me,” said Mr. Weasley, looking extremely agitated as he glanced over his shoulder as though making sure they could not be overheard. “Trying to find out whether you’d been expelled or not. I’ll leave a note for Dumbledore when I drop you off, he ought to know Malfoy’s been talking to Fudge again.”
“What private business have they got together anyway?”
“Gold, I expect,” said Mr. Weasley angrily. “Malfoy’s been giving generously to all sorts of things for years. . . . Gets him in with the right people . . . then he can ask favors . . . delay laws he doesn’t want passed . . . Oh, he’s very well connected, Lucius Malfoy. . . .”
So Arthur believes this was basically your run-of-the-mill corruption of political institutions and bureaucracy through bribery. But contextually-speaking, were there particular things that Lucius was asking for that were relevant to the upcoming war and strengthening Voldemort's new effort? Anyone have any insight or inferences based on other dialogue and the rest of the narrative of the book?
Also, what was the conversation in the movie? Was Lucius attempting to influence the results of the court case? Or were they possibly talking about another matter? Maybe both?