The musician, who was also part of progressive rock group Emerson, Lake & Palmer, died on December 7 after suffering from cancer.
Manager Stewart Young wrote on Lake's official website: "I lost my best friend to a long and stubborn battle with cancer.
"Greg Lake will stay in my heart forever, as he has always been.
"His family would be grateful for privacy during this time of their grief."
His death comes nine months after that of former bandmate Keith Emerson.
Emerson was found to have shot himself in the head, a Los Angeles coroner said.
A statement from King Crimson's record label, DGM Live, said they sent their "condolences and respects to Greg's family".
Lake was deemed a giant of progressive rock for his work with King Crimson and Emerson, Lake and Palmer.
Formed in 1967, King Crimson were seminal in the genre, with 1969's In The Court Of The Crimson King deemed their most successful and influential album.
After Lake struck up a friendship with Emerson - at the time a keyboardist for The Nice - the pair teamed up and recruited Carl Palmer to form the prog supergroup in 1970.
The trio went on to sell over 48 million records with Lake producing a number of their studio albums.
He was born in Poole, Dorset, in November 1947.
According to his website, Lake last performed in 2013 during his Songs Of A Lifetime Tour.
Genesis guitarist Steve Hackett paid tribute to Lake, posting on Twitter: "Music bows its head to acknowledge the passing of a great musician and singer, Greg Lake."
Yes keyboardist Rick Wakeman posted: "Another sad loss with the passing of Greg Lake ... You left some great music with us my friend & so like Keith, you will live on."
John Wetton, who was lead singer in King Crimson after Lake left for Emerson, Lake and Palmer, said: "And now, I'm so sad to hear of the passing of a musical giant in my genre. Yesterday, my dear friend Greg Lake died from cancer. RIP."
Radio DJ Lauren Laverne wrote: "Oh, man. Greg Lake. Awful news."
To non-prog rock fans, Lake was widely known for his hit I Believe In Father Christmas, which reached number two in the charts in 1975.
In an interview with the Guardian last month, which was published after his death was announced, Lake said the track was about Christmas becoming commercialised.
He said: "When Pete Sinfield and I wrote I Believe In Father Christmas, it was about how Christmas had deteriorated and was in danger of becoming yet another victim of crass corporate financial exploitation.
"As much as I love everyone having a good time, it's about more than 12 pints of lager and a crate of Baileys.
"It's more important to make some spiritual human contact, or visit someone lonely."