Freud, a grandson of Sigmund Freud, the inventor of modern psychoanalysis, was widely seen as Britain's top contemporary artist. He died peacefully in London on Wednesday, aged 88.
Freud was known for his signature nudes and self-portraits such as the powerful 1993 work of himself as a naked older man waving his brush like a weapon.
In recent years his paintings have sold for astronomical sums. His 1995 portrait "Benefits Supervisor Sleeping" fetched 33.6 million dollars at a Christie's auction in New York -- a world record for a living artist.
His lawyer Diana Rawstron said: "The funeral will be private and for the family only. There will be a memorial service at a date to be announced."
No date has been set for either event.
Sue Tilley, who posed nude for "Benefits Supervisor Sleeping", said she cried when she heard the news of Freud's death.
The artist gave her several etchings, which are potentially worth a small fortune, but Tilley said: "Money's not really important. Don't you think in life sometimes experience is more important than financial gain? Because of this painting I've had fantastic experiences."
The portrait is typical of Freud's warts-and-all style, but Tilley said she watched the work being created and so was not surprised by it.
"I saw it all the time because it's so huge, you would see it while he was painting it. He's not behind it, so it's in front of you the whole time, so I got very much used to it," she told BBC television.
Born to architect Ernst Freud, Sigmund's youngest son, in Berlin in 1922, Lucian moved to England with his family aged 10 to escape Nazism and became a British citizen in 1933.
His art career was interrupted when he served as a merchant seaman in an Atlantic convoy in 1941.
After an early flirtation with surrealism, Freud turned to portrait painting, particularly nudes, in the 1950s.
Copyright AFP (Agence France-Presse), 2011