This may have something to do with the fact that she was over 183cm tall by the age of 12; which also explains why she is so good at making clothes for women who do not necessarily fit an industry norm. "I had to learn to sew when I was growing up," she says, "because nothing else fitted me.
I used to spend hours at the local store, leafing through big books of Vogue and Butterick patterns, and then order one of them. By the time it was delivered I was really excited." She also became adept at adapting second-hand clothes from thrift shops.
"I remember finding a black silk 1950s dress, taking it home and unpicking the waistband and the seams, then sewing it together again, so that it would fit me."
If a meticulous attention to detail is the underpinning of Scott's career, so is her ability to reinvent herself, while revealing no more trace of what lies beneath (the bumps and lumps of ordinary life) than do her sleek sheath dresses.
The child of a traditional upbringing - her father worked in insurance, her mother at the local bank - she has retained her parents' work ethic, even as she left her home town far behind her. One of the words that she uses about herself is "frugal" - she avoids the extravagant waste of material, and other resources, as a designer - which possibly fits well with Mick Jagger, a rock star with a firm grasp of financial management (his ex-wife, Jerry Hall, has also said of Scott, "I think she's better at dealing with him than I am").
But it was fashion, rather than frugality (though a pinch of this may have helped), that provided Scott's route out of Utah.
At 17 she was spotted by the photographer Bruce Weber, who told her she could find work as a model, if she bypassed New York ("he said they wouldn't 'get' me there") and headed straight for Paris. She bought a one-way plane ticket, using her savings from babysitting jobs, and arrived without contacts, friends or a word of French. The name change came soon afterwards, but it was her striking beauty and unfeasibly long legs - 106.7cm - that got her a booking for a Chanel couture show, swiftly followed by other catwalk appearances. In retrospect, she says, the insight she gained into the craft of fashion (the couture fittings, the skill of Parisian pattern cutters and seamstresses) gave her more pleasure than modelling: "I didn't particularly like being objectified."
Hence her move away from the gaze of the camera - while also remaining firmly on the side of the women being photographed - when she moved to California in 1994, to work as a stylist with Herb Ritts, for Vanity Fair and Rolling Stone (among others; indeed, it was on a shoot that she first met Mick Jagger). Scott's reputation as an expert adviser on what to wear and how to wear it began to spread within Hollywood circles, enhanced by her costume designs: for Sharon Stone in Diabolique, Ellen Barkin in Mercy (and later Ocean's Thirteen) and Nicole Kidman in Eyes Wide Shut. All of these clients have remained longstanding advocates.
"L'Wren and I have been dear friends for years now," says Kidman, in an unusually speedy response to my request for a comment. "She knows what aspects to accentuate in a woman, and is able to make you feel incredibly sexy and sophisticated when you are in one of her exquisite designs."
Sarah Jessica Parker is similarly enthusiastic: "I think L'Wren has an extraordinary ability to make dresses that genuinely flatter a woman. She makes an unbelievably contemporary dress in a remarkably old-fashioned way for all sorts of women and body types." And Christina Hendricks, another of Scott's loyal clientele, is equally swift to join the chorus of approval: "L'Wren's clothes make you feel like a sexy pin-up, a sophisticated lady and a rockstar all at once. She designs for how women want to look and for what men want to look at."
All of which means that by the time I meet Scott, I am hoping for some of her renowned astute sartorial advice.
Forget Scott's relationship with Mick Jagger (though credit must be given to him for choosing an independent woman with a career of her own), her aficionados are more interested in discovering how she can supply them with a defined waist and bottom, without demanding regular attendance at the gym.
Here, then, are some of Ms Scott's suggestions: wear nude shoes with a little black dress if you want your legs to look longer; a midnight-blue indigo wash will make jeans seem darker than black; a crisp white cotton blouse is a shortcut to appearing fresh, but a black taffeta version also has merits; don't obsess about separating gold and silver accessories. As it happens, she mixes both, wearing several Victorian bracelets on each wrist ("they're like my Wonder Woman cuffs - I like a little bit of armour"); ditto handbag trimmings and jewellery, though her new range of bags (named after her mother, Lula, "who always carried a bag with her to work every day") solves the problem by using "gunmetal grey hardware, that disappears against a light or dark colour."
Scott also displays an eagle eye for what is flattering (a feature sometimes lacking in an industry that values the shock of the new over the realities of a womanly silhouette). When we meet I am wearing a billowing faded silk T-shirt with jeans, and, although she is far too polite to comment on my outfit, when I press her she remarks, "I could say, Justine, you should try a Headmistress dress, but if you're not comfortable in it, then it's not right for you."
Immediately, I want to try on the aforementioned dress - Mrs Obama looks both powerful and composed in hers - and Scott is kind enough to oblige.
So here I am, undressing behind a screen in her studio while she disappears through a wardrobe door, which turns out to lead into another concealed room ("It's my own version of Narnia," she says, before closing the door behind her). Tactfully, she also whisks out a far more flattering bra than mine (from John Lewis! Who knew!); and when I ask if I should be wearing big knickers to flatten my middle-aged spread she says, reassuringly, "Oh, no, you don't need control underwear to do the work of a zip - that's what the dress is for."
And what a dress it is: fine black wool, three-quarter-length sleeves, discreet black sequins around the cuffs and neckline; buttons that can be unbuttoned to reveal a slit at the back of the skirt (a clever combination of sexy and demure); just below the knee, which turns out to be far more flattering than expected - and the fit is remarkable. For the first time in my life, not only do I have a waist, but suddenly I seem to have acquired a more ample bosom, and a pert bottom. This seems to me, in all the circumstances, pretty close to a miracle.
The Headmistress dress also turns out to be comfortable - I can walk in it, and sit down, and it feels containing, rather than constricting; more proof of Scott's skilful design. "You can celebrate the female form in comfort," she says. "We left corsets behind in the dark ages, so why bring them back now? The modern woman has a modern life, and most of us work. There's no time to change before we go out in the evening, so a dress should always look appropriate for day and night."
Her own dress - a black-belted design, also with three-quarter-length sleeves - fits this prescription; and as a woman in her 40s, Scott understands why we might not want to bare our arms.
"I've never met a woman who thinks they've got a good enough figure - however perfect they look - which is sad, because no one else can see these perceived flaws; they're entirely internal.
"But I feel I've succeeded if I can design a dress that you can always rely on, that will stand the test of time, that becomes like a dear friend."
Such a dress doesn't come cheap - upwards of £1000 ($2087) - but it won't date, as is evident from the continuing appeal of the designs from her first collection, launched in 2006 (although she was already making individual pieces before then, for clients who needed something unfussy to wear on the red carpet). You can see why other designers rate Scott so highly; Lanvin's Alber Elbaz has observed, approvingly, "Her eye is almost like a camera. When I'm designing, the mirror can show me things I can't see with my own eye. She's like that, but what you see in the end is the person, not the dress - that is the forte of L'Wren."
Scott herself describes her work as being intrinsically practical: "Sometimes people can lose sight of that, but I'm not trying to create a revolution every season - it's an evolution. Because you have to think about your customers - they're a huge variety of women, from across the world, with different needs, and in different shapes and sizes."
It sounds simple, but then simplicity is too often forgotten amid the frothy embellishments and grand gestures of high fashion.
In the capable hands of L'Wren Scott, however, such straightforward common sense begins to look, however surprisingly, like the height of luxury.
