They said in a statement after her death: “She had a sharp mind, and when she spoke it, she did so eloquently. She was courageous and, at times, outrageous, with a mischievous sense of humour.
Despite Lady Lucan’s severance of ties her family said they remembered her “lovingly and with admiration”.
The charity told the newspaper the proceeds will “help us to continue fighting bad housing and homelessness”.
Camilla Bingham, a QC, told the after an inquest held in London: “Mummy left her estate to the homeless charity, Shelter.”
The 80-year-old was found dead at her home in Westminster, central London, by police in September after she was reported missing.
Lord Lucan vanished following the discovery of the body of nanny Sandra Rivett at the family’s home at 46 Lower Belgrave Street, central London, on November 7 1974.
The aristocrat is said to have killed herself with a cocktail of drink and drugs after wrongly self-diagnosing with Parkinson’s disease.