A photo-shoot with Leibovitz has long been the Hollywood equivalent of a lifetime achievement award, reserved for established A-listers. Donnelly is not quite at that level yet but her dark-eyed intensity has won rave reviews from New York's ferocious theatre critics and there is no doubt that her star is in a steep ascent. The petite, almond-eyed Belfast actress has also been on our screens in The Fall, where she plays a solicitor who is stalked and murdered by Jamie Dornan's serial killer. She giggles when told that one reviewer referred to her character as 'lucky' - "I think that they might have been more referring to how incredibly good-looking Jamie is" - but says that her own life has given her some insight into the unsavoury attentions of strangers. Dozens of websites have taken it upon themselves to feature mash-ups of her most compelling sex scenes and when she was starting out as an actress she had admirers hack into her social media accounts.
"I've had people break into profiles on my internet, they got into my accounts, this was at the beginning of my career," she says. "There is a fair bit of alarm when something like that happens. It definitely bothered me a lot at the time. But you move on from these things. I reported it to the relevant people and then I didn't worry too much about it because you can't live your life in fear. I've been reticent to get involved in that side of things. It's not my job to get really personal in how I express myself. I've met fans and they've been lovely. But letting my personal life out there, I don't think is a good idea for me, I think the more you do that, the more you can be accused of encouraging that kind of attention." On her Twitter feed she makes the message ever clearer: direct messages will not be entertained.
As her fame has soared her romantic life has also come under some scrutiny. She went out for a couple of years with Snow Patrol bassist Nathan Connolly - for a while they were one of Northern Ireland's ultimate celebrity couples. But she confirms to me that the relationship has been over "for some time" and she has a new love in her life, although she doesn't care to name him. "I do have someone else on the scene. He's sort of half civilian, half industry person; he's a writer. It's all going well. It's great to have someone who understands the life we (actors) lead a bit."
Despite (or perhaps because of) the prurient fascination with her love scenes and love life, Donnelly has a slightly prim and proper air. From the very start of her career, she tells me, she firmly ruled out appearing in any lads' mags and it's no surprise to learn she is a former convent girl. "I did 14 years there," she laughs. "But by the time I was an adult I didn't massively feel that (Catholicism) had a huge bearing on my life. I suppose it was more cultural than religious as such. But when I talk to my friends now, who grew up in England and Scotland, where convents maybe aren't as prevalent, it does feel that it was a stricter upbringing that I had."
The Troubles formed what she makes sound like a slightly distant background to her childhood and she says she was shielded from the worst of the conflict. "They formed the same backdrop that anyone growing up in the 1980s in Belfast would have had, which is to say that it was always there but it was the same for everyone. It was always on the news and I suppose that tension and fear that people felt did colour the atmosphere of the place a bit. I consider myself fortunate in that it didn't leave me with scars which I had to struggle with."
The stifling atmosphere of the North, of which Patrick Kavanagh wrote so well, was not alien to her, however: "I will say that in those years there was a real sense that do to what you wanted to do, to become successful, you would have to leave Belfast. I can specifically remember telling a teacher in my school that I wanted to become an actress and he told me to get my head out of the clouds. There was a lot of fear in the city in those years and people did feel held back. I did feel that I had to get out to fulfil my potential and to be myself. And so I did that I went out and learned a lot about the rest of the world. When you're very young you can be quite dismissive, you just want to get out and try things and hopefully make a name for yourself. But as you get older you mellow a bit. I think (leaving) gave me a lot of compassion for the place I'd come from. It gave me a lot of empathy."
She went to study in Scotland, (where most of her family lives now, having moved one by one after Laura left Northern Ireland), and attended the Royal Scottish Academy, Glasgow. She made her small-screen debut in 2005 in Julie Burchill's semi-autobiographical Sugar Rush, playing the central character's lesbian love interest in two episodes. She also starred in Best: His Mother's Son, the BBC drama on the life of George Best, playing Best's sister Barbara. Her first big break Stateside came in the American mystery drama Missing, where she had a part in the series, which starred Sean Bean and Ashley Judd. The series garnered absolute raves reviews from critics but was less popular with audiences and it was no surprise when it got cancelled. "You always have hopes for work like that, the possibility of it going on for several years was really exciting, particularly after what was written about it", she says. "It was also the first American series I'd done. But I had a healthy level of scepticism about it lasting because these things can end and that's just the way the business is."
Winning the role of Jenny in the time-travel fantasy Outlander was another coup, given the cult success of the series, which is based on the novels by Diana Gabaldon. Much of the action takes place in her on-screen husband's ancestral home, Lallybroch, causing her to be christened 'Jenny from the Broch' by adoring fans on Twitter. It gave her what was surely one of the best lines of dialogue of her career, which surely comes in handy in regular life at times: "Do I have to grab you by the bollox and make you stand still to listen to me." Outlander also reunited her with Sam Heughan, who plays her character's brother in the series.
Donnelly and Heughan attended drama school together, and she says she was thrilled to be reunited with him for the role. "We always knew he was destined for great things", she says. "I had also done a film with him in Norway over the summer and I was with him when he found out he was getting the role, so that was amazing." She says she hasn't read too far ahead in Gabaldon's novels because she wants the drama to be fresh in her head as she prepares for each scene. "I'm about to get started on the second book as I'm about to start filming that at the end of this year and I don't want to know any more beyond that."
The up-and-down nature of acting exacts a toll, she says. "The unpredictability of the work can be difficult, you might be worrying where the next gig is coming from. I've been busy with work, thank God, but you still never know where the next gig is coming from and if you're not careful you can fret over things. It can be struggle to make time for some things that are really important, like people, like family, but you have to develop the knack of just letting go and trying not to be in control all the time because if you wanted your life to be predictable you shouldn't have gotten into acting in the first place."
She was helped in her quest for Zen, she says, by Hugh Jackman who she played opposite on Broadway in the short and elliptical Ian Rickson-directed play The River. They had great chemistry on-stage and off; she tells me that while preparing for the run they went fly fishing together. "We went upstate to do it when we were about to begin rehearsals, which was amazing, the scenery was just incredible. I caught the first fish, I should point out, I was so proud. Fishing is very meditative, you need to be able to give up control and cast out the line and then hope for the best, so in that way it's quite like acting. It definitely got me in the zone for the play."
The bonding moments would pay off on the stage. The theatre critic for The Chicago Tribune wrote of her performance that Donnelly "revealed a juicy joie de vivre, which (she) embodies with delicious excitement … she is a great rush of everything at once." Reviews like that brought agents knocking on her door all at once, and she soon landed the part in one of the most hotly anticipated films of the year, Stephen Frears' Icon, in which she plays Lance Armstrong whistle-blower Emma O'Reilly.
The US Postal cycling team's soigneur recently wrote a book in which she depicted herself as the sole female jostled on all sides by marauding male egos. Donnelly never met O'Reilly, who was under contract with another documentary during the period the actress was researching the role, but the Belfast woman says she could certainly relate to the sentiment. "I could very much identify with that. Emma was a woman in a man's world. While there are obviously a lot of women working in the acting world they still have to fight harder than men do in this profession. There are fewer jobs and few opportunities, and there is a real sense of struggle for a woman doing this. And then you add on top of that the physical pressures, which are particularly faced by women, the expectation that you have to look great to do a great job, I mean I could talk about that all day. So yeah, the challenge for Emma was to try to make it in this man's world and at the same time keep her integrity. She had this whole machine against her. Ultimately (blowing the whistle on Armstrong) was a really painful choice for her to make, but that made for great drama and it was a really interesting role to play."
Donnelly says that sexism is still rife in Hollywood, as demonstrated by the recent revelations in the Sony leaks. "I think that it's a shame that we're still at that point where we have to fight for that equality. How many more generations will it take? You have Angelina Jolie who can top box offices and is a wonderful actress, and at the same time she's having judgements that were written about her in those (Sony Leak) emails. And I think if she were a man there's every possibility those emails wouldn't have been written in the first place. If a women has strength or drive she'll be judged for that in a negative light, whereas for a man those are seen as admirable ambition."
While her work has generally been acclaimed, she tells me she tries to treat triumph and disaster as two imposters. "I generally don't read reviews but it can sometimes be a difficult thing to avoid and you often get a sense of how something has been received by the reaction of the people around you. You never want to sound bitter about critics, because they're entitled to do their job too, but I place much more trust in a person who I can look in the eye and someone who I know I share some kind of taste with - so my friends for instance. For me, a critic is unknown and therefore irrelevant."
Her family have moved to Scotland in recent years but, after a stint filming a TV mini-series adaptation of Beowulf in Newcastle, she says that her plan is to return home.
"I'm actually in the process of looking for a property somewhere in Ireland", she says. "I'd like to live here with my boyfriend. There is a lot going on in my career at the moment but maybe being away has made me a bit nostalgic. Ireland is a place that poets and playwrights have written about for generations and for me it's magic too; I'm ready to come home."