Last year she ended up in Whitehall, leading a delegation to apologise to John Prescott after Danbert Nobacon of Chumbawamba doused the Deputy Prime Minister with the contents of an ice-bucket. Mr Prescott duly lectured Ms Anderson and various record company chiefs about the discourtesy to him and his "womenfolk".
The previous year, Anderson had been obliged to protect Jarvis Cocker physically, from both the police and (far more threatening) Michael Jackson's choreographer, who had fallen upon him menacingly after Cocker invaded the stage to wiggle his bottom in protest at Jacko's messianic set.
"I saw Jacko's people coming after him," she recalls, "and the choreographer didn't look at all friendly. So I said, 'Now come on Jarvis, you come to the dressing- room with me', and I managed to look after him."
But you can't win them all. When Fleetwood Mac last year insisted that their dressing-room area be painted beige, she gave in, recognising that the band was stuck in a Seventies time-warp. But generally, she wins.
No one in the music business will be surprised at that. Certainly not Geri Halliwell. As soon as she parted company from the Spice Girls she rang Anderson and asked her to be her manager. Geri knew Anderson to be the most influential woman in the music business, but hers is a name that few outside the industry would recognise, and her face is unknown to the general public.
Which is a pity, because the British music scene, not always big on humour or humility, has probably never had a more human face, or a more down- to-earth role model. The only thing remotely scary about her is her laugh - a fruity chuckle, which increases in heartiness as it reaches its climax: a laugh that began in a Hertfordshire girls boarding school, was developed at the Pony Club and was perfected at a finishing school in Switzerland.
Anderson was brought in to remould the Brits eight years ago. The event was a joke at the back end of the Eighties. It's possible now to feel nostalgia for Samantha Fox and Mick Fleetwood's performance when the autocue broke. "Here are The Four Tops," announced Sam, and on came Boy George. "Hello, I'm the One Top," he said.
Worse, as Anderson quickly discovered, it made only pounds 10,000 in 1990 and there were constant accusations of vote-rigging by the record companies. It now brings in pounds 300,000 a year to help fund the Brit School for young musicians, and other charities. She has democratised the voting structure, sees that the brochure is sold in 2,500 UK shops and has switched the television contract from the BBC, which didn't pay, to independent television companies, which do.
Finishing school had already made her a distinctive voice in record company land. "When I came into the industry 20 years or so ago, everyone still found it necessary to speak like David Bailey," she says. "But I just couldn't be bothered with all that. I talk posh. I'm middle class. That's the way I am. I'm not going to disguise it."
Nor has she been prepared to kowtow to the attitudes of an industry that even now, for all its business and exports prowess, can be adolescent in its attitudes to women - not least the sales conferences she had to attend, which were often preceded by the statutory soft porn videos. "They'd say to me 'where's your sense of humour?' I'd reply, 'evidently not in my cock'. The music industry tends to enjoy going into a clan, into a posse. And women tend not to do posse. It was going on all around, lots of bonking on sofas and other extracurricular activities. But I never got involved in all that. When Richard Branson tried to throw me into the swimming-pool, I simply glared at him and said: NO, Richard! I've been to public school, I've done all that, been there. Don't."
Branson asked her to join Virgin, soon after she had left Chrysalis at the age of 23. There she had been assistant to the boss, Chris Wright (music-industry-speak for buying his presents and his furniture and delivering his dry-cleaning). She arrived at Virgin just as punk was dawning, with its bile, spit and vomit. Vomiting is not her style, however, and she concedes that she has only ever thrown up twice, out of nerves: "Once was the day I became managing director of RCA Records. The other time was when I had to go to court to give a character reference for Johnny Rotten."
Punk may have died that day (Anderson says she testified to the effect that Rotten was too weedy to hurt anyone), but Anderson's career continued apace. As managing director of RCA, she was the first woman to achieve the top position in a record company in Britain. While there, she insisted, against much opposition, that the parent company BMG introduce a 12-week maternity leave and child allowance agreement for all female workers. She also introduced two weeks' paternity leave, but insisted that it be taken within a month of the birth, "not saved up for the rugby tour".
Two years later she was sacked. "I'm not very good at corporate politics. I tend to say the wrong thing, like what's really happening. Wrong! Chairmen want to hear that this record is so great. They do not want to hear you say that this record is a bit of a turkey. Also, we didn't make up the numbers they wanted. Eurythmics split up, Fairground Attraction split up, Rick Astley failed to deliver his album. Not my fault, really."
As it happens, on those issues where she took a stand, pop history has proved her right. "They weren't at all sure they wanted to sign M People, but I signed them and they haven't done too badly. And the dance boom was just getting going, but the major record labels weren't interested in it... I thought it was really exciting and invested a lot of money in it, and started a subsidiary dance label. I was a bit of a dance girl."
She is now married to her second husband, David Campbell, the former manager of UB40 and older brother of two members of the band. She was previously married to Bram Tchaikowsky, who was a guitarist with the late- Seventies power-pop group The Motors, who had a hit with "Airport". At their 15th- century Kentish mansion David plays the role of house-husband. "I made a decision not to suffer from guilt about jet-lag or about leaving the children," says Lisa. They have two children, Hereward, 14, and Hannah, 11, who in fact see their mum quite a lot and enjoy little bonuses - such as occasional calls from the erstwhile Ginger Spice.
"I was surprised when she approached me," Anderson says of Halliwell. "I had said hello to her at the Brits, but we didn't really know each other. She is a very impressive young woman, very focused on her new direction." The new direction so far has involved a UN ambassadorship, a song at Prince Charles's 50th birthday party and a well-received appearance on Parkinson. Significantly, the one dubious image of Geri - Baroness Jay citing her as a role model for schoolgirls - had nothing to do with either Anderson or Halliwell. New Labour made up their own minds there.
Now Anderson, who knows more about the record business than most, is renegotiating Geri's record contracts. That won't delight the record companies, as she is known as a tough negotiator. Jonathan King, who presented the Brits pre-Anderson, and now snipes from a distance, calls her "Lethal Lisa".
"I'm not aware of how people perceive me," she shrugs, "I can be pretty scary. But I weep under tables, too." Undoubtedly, her control of the Brits is meticulous. And, much as she likes a bit of pop madness to enliven the ceremony, she is not taking too many chances tonight, especially as a major campaign to persuade world leaders to cancel Third World debt is being launched at the Brits.
Quietly, she has made sure that the Cabinet ministers and Cherie Booth will be seated in boxes which only accredited waiters may enter with an ice bucket.