The British rock star, who was born Ian Fraser Kilmister in Burslem, Stoke-on-Trent, died on 28 December, aged 70, just two days after discovering he had an "extremely aggressive cancer".
Fans have been asked not to attend the service at Forest Lawn Memorial Cemetery.
A live stream has been put on YouTube and people are being urged to watch together in a bar, club or at home.
More than 245,000 fans are currently viewing the service online.
A message from the band said: "Wherever you are, please get together and watch the service with fellow Motorheadbangers and friends."
The service began with an introduction by Motorhead's manager Todd Singerman, who welcomed the guests to the "celebration of Lemmy's life".
"We all know he would not have stood for anything formal or sombre," he added.
Lemmy's son Paul recalled his father's life as a "stage warrior" and "free spirit", and Motorhead drummer Mikkey Dee also gave an address.
Obituary: Lemmy
Lemmy formed Motorhead in 1975 after being thrown out of space-rock band Hawkwind, and went on to record 22 studio albums with the band.
His ferocious bass playing and his appetite for drink, drugs and women earned him a reputation as one of the wildest frontmen in rock.
At the time of his death, Mr Singerman told BBC News the star had had cancer "in his brain and neck" and that his sudden death had come as "a massive shock".
He said Lemmy, who turned 70 on Christmas Eve, had died while sitting in front of his favourite video game with his family.
Mr Singerman described Lemmy as "the pinnacle, he's up there with one of his idols, Elvis".
He added: "He was one of the last true rock stars left, this guy lived it every day."
Lemmy was known for his penchant for whiskey and cola, but Mr Singerman joked that in recent years, the frontman had "switched to vodka and orange - he thought it was healthier".
"He was one of the kindest men I ever met - he was the people's man."
Those paying tribute included Ozzy Osbourne, Queen's Brian May, Metallica and Kiss star Gene Simmons.
Since his death, more than 100,000 fans have signed an online petition for the singer's nickname to live on through a newly discovered chemical element, which they have asked to be named "Lemmium".
The funeral of Motorhead frontman Lemmy is taking place in Los Angeles.