We're in the living room of a hotel suite in Manhattan and Tyler, having kicked off her very high heels, is lying on a sofa as we sip pink Champagne. She is concerned, however, that her horizontal position - and the aforementioned softness of her voice - might mean my dictaphone fails to catch every word, so she has thoughtfully perched it, giggling, on her bosom.
We are here to talk about The Leftovers, the HBO series based on a book by Tom Perrotta, that rescreens as a book set on Sky TV here next month.
Tyler plays Meg, a troubled young woman dealing with a devastating loss ... but she's far from the only one. So is the rest of the town of Mapleton, and beyond, after the sudden, unexplained disappearance of 2 per cent of the world's population.
"This terrible event has happened, but it's three years later, and the story is not really about the event itself," Tyler says. "It's about human beings and their journey and their pain."
The 10-part drama, which also stars Justin Theroux and Christopher Eccleston, has a surreal quality that has led to comparisons with the about-to-be remade Twin Peaks.
But the grief afflicting the town's population is borrowed from a much more grim reality - 9/11.
"Like other huge world events, it seems to divide history in two; there is the life before it, and the life after it," says Perrotta. So the unravelling of relationships and family bonds in The Leftovers can be read as metaphors for the social and political fracturing of American society after 9/11.
When it came to adapting the story for television (Perrotta co-wrote the script with Damon Lindelof, co-creator of Lost), another, more recent, tragedy strongly informed the mood of the show: the Sandy Hook school massacre in Newtown, Connecticut, in December 2012, in which 20 children and six teachers died. "For the people in that town, it feels as if life will never, ever be the same again," Perrotta says.
Meg deals with her grief by abandoning her fiance and joining a mysterious sect called the Guilty Remnant, who dress all in white, don't speak, and chain-smoke as a mortification of the flesh.
Tyler's own way of dealing with grief is "very quiet and sad and rational. I feel a lot. But I'm also very resilient," she says.
It's a television debut for Tyler, whose acting career so far has been confined to the big screen. In her teens, she starred in independent films including the comedy Empire Records and That Thing You Do before making her name in Bernardo Bertolucci's dreamy, Tuscan-set Stealing Beauty.
In her 20s, she was perfectly cast as Arwen, the elf maiden in The Lord Of The Rings trilogy, and appeared in other big-budget hits, such as Armageddon and The Incredible Hulk. In her 30s, however, she has seemed to step back somewhat from the screen.
"Ever since Milo was born, I haven't really been making many movies because I just can't imagine being away from home for long periods of time," she says.
Milo, her son with her former husband, Royston Langdon, of the British band Spacehog, is now 9, and with The Leftovers filming in and around New York City, Tyler has been able to fulfil her domestic duties at home in Manhattan's West Village as well as work.
Liv Tyler with co-star Viggo Mortensen in The Lord Of The Rings.
"It's a steady job, and that's something I've never had before. It feels like such a luxury. It has its challenges, too. "There's something incredibly freeing about being 25 and getting on a plane to New Zealand, and being able to immerse yourself completely in your work," she says. Tyler sits up and shakes out her mane of dark hair. "Now, I get up and make Milo breakfast and walk him to school, and then I have to go and beat somebody up at work, and then figure out what's for dinner. It's a different kind of balance. It's the more grown-up version of being an actress."
Her decision to put her home life ahead of her career in recent years is a direct reaction to Tyler's own early experiences. "From a very young age I had this idea that if you are very successful in your career and you're giving all of your attention to that, then your family life ... possibly will not flourish as it might."
Tyler was raised by her mother, the model and groupie Bebe Buell, who was the inspiration for Kate Hudson's character in Almost Famous, and whose close friends included Mick Jagger and John Lennon.
Famously, Tyler discovered at the age of 10 that Aerosmith frontman Steven Tyler was her father, after meeting him backstage at a gig and noticing a resemblance between herself and his daughter, Mia (her likeness to Tyler - with the same pillowy pout and dainty ski-jump nose - is glaringly obvious). Until then she had believed her father to be Buell's on-off partner Todd Rundgren, also a musician.
When Buell confirmed her daughter's suspicion - while Tyler was onstage - she recalls that the 10-year-old simply smiled and said: "Christmas is going to be really fun this year."
However, it was not the most ordered of childhoods. "My mum was very young [24] when she had me, and she didn't necessarily have all her tools in her toolbox," Tyler says. "We kind of grew up together, which was a beautiful thing. But we moved around a lot, too, between Maine and New York, and it was hard for me."
As for her newly acquired rock star dad, she has said in the past that "I don't think he was in any position to be a father".
Tyler and Aerosmith frontman Steven Tyler. Liv discovered he was her father when she was 10. Photo / AP
When she was born, Steven Tyler was in the throes of his well-documented drug excesses. Rundgren was apparently aware of her paternity but, believing she needed a father, agreed to participate in the deception. "What an amazing thing Todd did for me. Luckily, it just made me feel more loved. I had two dads instead of one."
Tyler began modelling in ads at 14, though, she says, she loathed it. "I just didn't like being told what to do," she says. "It was silly and rebellious of me. I should have enjoyed it more. But I have a very hard time with authority."
She has no problem respecting her directors on set, she says. "But when I was 14, I had so many ideas, and I just had to stand there and look pretty and not talk a lot. I didn't like that very much."
For the past decade, having overcome her dislike of the job, she has been contracted to the cosmetics giant Givenchy.
"I love modelling these days, and I miss doing it now that I'm not. I was always popping over to Paris," she says. Unusually for a model, she confesses to "always" being on a diet, but today looks svelte, in the tightest of skinny jeans, a peach blouse and white tuxedo jacket.
At 16, Tyler won one of her first acting roles courtesy of her father, alongside Alicia Silverstone in the video for Aerosmith's Crazy. Her first film role came a year later, in Silent Fall, followed by Empire Records.
"I started really working right at the point when I probably would have become a f***-up," she says. "In those last three years of high school, you get really naughty and everything can go wrong. I'm grateful to my mother because, instead of that, I started travelling all over the world and working with incredible people, and I became very focused and disciplined. When everybody was doing acid and partying like crazy, I was at work on a movie in Tuscany."
That film proved to be her breakthrough, cast by Bertolucci as the lead in Stealing Beauty, also starring Jeremy Irons and Rachel Weisz.
Tyler is nothing short of rhapsodic when I mention the film, which was a coming-of-age for her as much as for her character, the lush, ripe Lucy Harmon.
"Nothing has ever compared to the experience of making that film. I graduated from high school the day before I went away, and turned 18 that summer. For my birthday, they roasted a pig for me, in the middle of a Tuscan farmhouse, with peacocks on the roof and bowls of cherries everywhere, and I was barefoot all the time."
Lucy travels to Tuscany desperate both to lose her virginity and to discover who her father is. Tyler has admitted that she attempted to separate herself from that particular storyline.
"I tried my damnedest not to think of my own situation," she has said. "But at one point, after a take, I just started to cry and cry. I remembered when I found out about my dad and how we just stared at each other from head to toe."
Stealing Beauty premiered at Cannes, where Tyler's face was plastered across billboards around the town, catapulting her into the limelight.
"When you start working at such a young age, everything is accelerated, and by the time you get to your mid-20s, you feel what most people probably feel in their mid-30s or early 40s."
She married Langdon at 25, and gave birth to Milo a year later. "In my 20s, I definitely had a sense of wanting to create stability for myself."
The couple divorced in 2008 after five years of marriage, but Tyler is impressively sanguine about it.
"The idea that we can share a roof with someone else forever is a beautiful notion, but it's much harder to actually do. I grew up in a very bohemian environment, and I always knew that it doesn't mean that you don't love that person, or that they're not important to you," she says. "But I'm completely devoted to Milo and our little family, no matter how eccentric it might seem to others."
In fact, Tyler has spent significant periods of time with Langdon's family in Leeds. "We had the best Yorkshire Christmas last year. It was so under the radar. And I'm so happy that Milo gets to have that in his foundation - the humour and the groundedness, those northern qualities.
"I think that's the one thing that's quite different from when I was a girl. I just lived with my mum, and it was her side of the family that helped out - my aunt and my uncle and my grandmother - and I would just go and visit my stepfather, Todd, and my Dad."
These days, she is close to Rundgren and Tyler, and sees them regularly, as does Milo. "He has a ton of grandparents - semi-normal ones in Leeds and then totally bonkers ones on my side."
She also believes strongly in "the family you create for yourself" which, in her case, means a close network of girlfriends who include Kate Hudson, Gwyneth Paltrow and Stella McCartney.
"This year, I've been so happy just being home and being a good mum and going to work - my plate's been perfectly full. I haven't wanted any seconds."
However, she admits to considering seconds when it comes to her family. "I hope I will have more children. I'm 100 per cent planning on it. If the stork could just drop them off on my roof, I'd be so happy - I'd have, like, 20."
She is in a relationship now, but whether she'll marry again is uncertain. "There's something interesting that happens in your 30s. You're not in the stage anymore of princes and happily ever after. It's a different stage of acceptance and realisation about the realities of love and relationships," she says.
"Forever is a long time."
The Leftovers box set screens on Sky TV's Soho channel from November 1.
