Ms Pinochet, who is being held at an immigration detention centre, is expected to argue that Chilean courts are unable to give her a fair trial and that her family faces political persecution in Chile.
"The instruments of the state are being used with the purpose of defaming and discrediting the honour of the people," Ms Pinochet said in a statement released to the Chilean media. "They [judicial investigations] don't seek to clarify the source of my father's funds, but instead some seek the total defamation of each and every member of my family."
The Chilean foreign minister, Ignacio Walker, ridiculed the asylum application, calling it "surrealistic" and "absolutely lacking any basis".
"I hope that Lucia Pinochet returns to Chile voluntarily, to appear before justice," said Mr Walker, who acknowledged that the case may quickly evolve into a cumbersome extradition battle.
He said that if the US rejected the asylum claim, Ms Pinochet would be returned to Buenos Aires where she would face an extradition request from Chile.
In Chile, Ms Pinochet faces criminal charges of tax evasion and using false passports to hide the family fortune, allegedly earned by illegal commissions on arms deals. She was cited to appear before a court in Chile earlier this week, but instead embarked on a four-day, transcontinental escape that took her to Argentina, Brazil and finally to Washington.
In a statement, Carmen Hertz, the prosecuting attorney in the tax evasion case, said: "This adds more infamy to the crimes of Pinochet and his circle.
"She went to Washington to move certain assets that have not been uncovered in the investigations."
It also adds a bizarre chapter to the already complicated legal situation facing General Pinochet, his family and top aides. While numerous human rights charges against General Pinochet stall in the Chilean courts, the investigation of financial crimes has devastated his family in recent months.
Pinochet family members and former top aides to the general are charged with hiding an estimated $27m (£15m) in more than 100 bank accounts scattered around the world. On Monday, four of the general's children, his wife, a daughter-in-law and two top aides were scheduled to appear in court. When they arrived, they were promptly arrested, charged and later released on bail - except for Lucia, who disappeared.
Chilean police immediately began monitoring her mobile phone, tracking her to Los Andes, a remote Chilean town near the border with Argentina. By the time border control officials were alerted, Ms Pinochet and her son had crossed into Argentina.
On Tuesday evening, Ms Pinochet boarded a United Airlines flight to Brazil and continued on to Washington. With her escape route now being monitored by Chile, Brazil and Argentina, a frenzied round of diplomatic manoeuvres unfolded as the US prepared to receive a fugitive member of the Pinochet clan.
Immediately upon landing at Dulles, Ms Pinochet was taken by the FBI and questioned, according to Chilean judge, Carlos Cerda. While she spoke with US authorities, Ms Pinochet rejected numerous attempts by Chilean consul Felipe Cousino and judge Cerda to speak with her and convince her to voluntarily return to Chile.
While Chilean officials press for a quick resolution of the situation, Ms Pinochet has several legal options which could keep her in America for months, effectively stalling the deportation procedure and transforming herself into the centrepiece of yet another international Pinochet legal drama.
With the election of the Socialist president, Michelle Bachelet, earlier this month, many Chileans had expected the shadow of Pinochet to finally be lifted. However, events in Washington may catapult the former dictator and his family back into the middle of Chilean foreign policy.
"If an extradition process begins and she does not voluntarily present herself, this will be a long episode," Ms Hertz said.
