It will now be cut and polished, Lucara said in a statement.
The highest bid in that abortive auction was $61 million.
Mr Graff said "The stone will tell us its story, it will dictate how it wants to be cut".
Reporting for the quarter as well as its half-year numbers today, in which interim earnings came in at eight United States cents per share compared to 17c at the interim in the 2016 financial year, Lucara said full-year production would be between 265,000 to 285,0000 carats compared to previous guidance 290,000 and 310,000 carats.
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"The only larger diamond previously unearthed was the 3,106-carat Cullinan Diamond, discovered in South Africa in 1905, and it was cut into smaller stones, the largest of which is the 503-carat Star of Africa, which sits in the Queen's Sceptre within the Crown Jewels".
Lucara had originally hoped to get at least $70 million for the stone, describing it as the biggest gem quality diamond found in more than a century.
The precious stone of 1.109 carats, discovered in Botswana in 2015, is now the property of the dealer british Graff Diamonds. "Our highly skilled team of master craftsmen will draw on many years of experience of crafting the most important diamonds, working night and day to ensure that we do justice to this remarkable gift from Mother Nature".
Lucara originally auctioned the diamond with a reserve price of $70 million past year, but bids at the Sotheby's sale only reached $61 million, Fortune reports.