The rock star, whose real name was Ian Kilmister, died just days after celebrating his birthday following a short battle with an “extremely aggressive cancer”.
Lemmy only received the shock diagnosis on Boxing Day, the band said.
His death comes little more than a month since that of the band’s first drummer Phil “Philthy Animal” Taylor. Lemmy himself led tributes to the 61-year-old rocker, who died on November 11.
Ex-Motorhead guitarist “Fast” Eddie Clarke, who played with the heavy metal group between 1976 to 1982, led tributes to Lemmy.
Clarke said on Facebook: “I have just been told that Lemmy has passed away in LA. Like Phil, he was like a brother to me. I am devastated. We did so much together, the three of us.
“The world seems a really empty place right now. I am having trouble finding the words ... He will live on in our hearts. R.I.P Lemmy!”
A post on the band’s Facebook page, which was also shared by the band’s current drummer Mikkey Dee, said: “There is no easy way to say this ... our mighty, noble friend Lemmy passed away today after a short battle with an extremely aggressive cancer.
“He had learnt of the disease on December 26, and was at home, sitting in front of his favourite video game from The Rainbow which had recently made its way down the street, with his family.
“We cannot begin to express our shock and sadness, there aren’t words.
“We will say more in the coming days, but for now, please ... play Motorhead loud, play Hawkwind loud, play Lemmy’s music LOUD. Have a drink or few. Share stories.
“Celebrate the LIFE this lovely, wonderful man celebrated so vibrantly himself. HE WOULD WANT EXACTLY THAT.”
The rock music world reacted with shock at the news.
Ozzy Osbourne, of Black Sabbath fame, tweeted: “Lost one of my best friends, Lemmy, today. He will be sadly missed. He was a warrior and a legend. I will see you on the other side.”
Kiss star Gene Simmons said: “Lemmy: Rest In Peace. Shake the heavens, my friend.”
Queen guitarist Brian May said: “Sitting here, Re-Tweeting, distracted, and wondering what I can possibly say about our utterly unique friend Lemmy’s passing. Ouch.”
Guns N’ Roses bassist Duff McKagan added: “Rest In Peace Lemmy. A hell of a man who suffered no fools. U shall be missed brother, and, THANK u 4 the years of unwavering kick ass R&R.”
Lemmy, who was born in Stoke-on-Trent on Christmas Eve 1945, founded Motorhead in 1975 after being fired from previous band Hawkwind.
According to the band’s website, his exit followed his arrest at the Canadian border for possessing cocaine, causing the band to cancel some of a US tour.
The Grammy-award winners are perhaps best known for their single Ace Of Spades, while the fanged face that appears on their album artwork has become one of rock’s most recognisable figures.
It took several years for the band to break into popular consciousness, which came when they achieved critical acclaim with the 1980 Ace Of Spades album, which reached number four in the UK chart.
The band recently celebrated their 40th year by releasing their 22nd studio album, Bad Magic, and were set to play dates in the UK and Europe over the next few months as part of a world tour.