L.A. Confidential

In early 1950s Los Angeles, Patrolman Sergeant Edmund "Ed" Exley (Guy Pearce), the son of the legendary LAPD detective Preston Exley, is determined to live up to his father's reputation. His intelligence, insistence on following regulations, and cold demeanor contribute to his isolation from other officers. He exacerbates this resentment by volunteering to testify in the Bloody Christmas case in exchange for a promotion to Detective Lieutenant. This goes against the advice of Captain Dudley Smith (James Cromwell), who states that a detective should be willing to shoot a guilty man in the back for the greater good. Exley's ambition is fueled by the murder of his father, killed by an unknown assailant, whom Exley nicknames "Rollo Tomasi".
Officer Wendell "Bud" White (Russell Crowe), whom Exley considers a "mindless thug", is a plainclothes officer obsessed with violently punishing woman-beaters. One such incident leads him to confront a former cop named Leland "Buzz" Meeks, a driver for Pierce Patchett (David Strathairn). White comes to dislike Exley after White's partner, Dick Stensland, is fired due to Exley's testimony in the Bloody Christmas scandal. White is sought out by Smith for a job in which they harass and beat up out-of-town criminals trying to fill the void left in Los Angeles following the imprisonment of gangster Mickey Cohen for tax evasion. The Nite Owl case, a multiple homicide at a coffee shop, becomes personal after Stensland is found to be one of the victims.
Detective Sergeant Jack Vincennes (Kevin Spacey) is a narcotics detective who moonlights as a technical advisor on Badge of Honor, a popular TV police drama series. He is providing Sid Hudgens (Danny DeVito), publisher of the Hush-Hush tabloid magazine, with tips about celebrity arrests that will attract more readers to Hudgens' magazine. When he becomes involved in Hudgens' scheme to set up actor Matt Reynolds (Simon Baker) in a homosexual tryst with L.A. district attorney Ellis Loew (Ron Rifkin), and Reynolds is killed as a result, Vincennes becomes determined to find the killer.
Three African Americans are initially charged with the Nite Owl murders, and later killed in a shootout. Although the Nite Owl crime initially looks like a botched robbery, Exley and White individually investigate it to discover indications of corruption all around them. White recognizes Nite Owl victim Susan Lefferts as one of Meeks' escorts which leads him back to Pierce Patchett, operator of Fleur-de-Lis, a call girl service that runs prostitutes altered by plastic surgery to resemble film stars. He begins a relationship with Lynn Bracken (Kim Basinger), a Veronica Lake look-alike prostitute. The body count rises when White searches a storage room under Lefferts' mother's house, and finds the decomposed corpse of Meeks.
When Vincennes approaches Smith with the evidence he has found with Exley, Smith realizes his scheme to take over Mickey Cohen's heroin empire is threatened. Smith shoots Vincennes, who utters "Rollo Tomasi" before dying, the origin of which Exley told Vincennes in confidence. Exley's suspicions are aroused when Smith asks him who Rollo Tomasi is. During an interrogation of Hudgens, Smith arranges for White to see photos of Bracken sleeping with Exley, which sends White into a rage. Confident that White has gone after Exley to kill him, Smith kills Hudgens. Exley investigates and discovers Meeks and Stensland used to work closely with Smith. White drives to the police station and begins to fight Exley, but Exley is able to convince White that Smith is corrupt and has set them both up. The two decide to team together to take down Smith. They are able to obtain evidence against Smith by threatening Loew, and later find Patchett murdered. Exley and White realize that Smith himself has been taking over after Cohen, and the killings have been Smith tying up loose ends.
Exley and White are set up with a trap against Smith and his hitmen. After a gunfight that kills all the hitmen, Smith shoots White in the face, but then is forced to surrender to Exley. As police arrive, Exley shoots Smith in the back, killing him. The LAPD cover up Smith's crimes and say he died a hero in the shootout to protect the department's image, and in exchange Exley bargains to also be hailed a hero and receives a medal for his bravery. Upon leaving City Hall, Exley sees Bracken, who tells him she is returning home to Arizona with White, revealing White survived the shooting. Exley and White shake hands and Bracken drives off into the sunset.

Question: Does Budd White sleep with Veronica Lake?
Answer: No, he begins a relationship with Lynn Bracken (Kim Basinger), a Veronica Lake look-alike prostitute.