Alfred Kinsey, the famous sex researcher, had a rule for those who conducted his intimate questionnaires. Don't ask: "Have you ever had sex with a goat?" he instructed. Always say instead: "When was the last time you had sex with a goat?" Or: "How often do you have sex with goats?" These formulations eliminated the element of shame, he explained, and allowed the interviewee to assume, at the outset, that anything might be considered normal.

I've often thought about this principle in relation to journalism - we tend to frame questions, unwittingly, in ways that can be off-putting to the interviewee - but I've never had an opportunity to ask Kinsey's exact question outright. Now, here before me in a north London restaurant, is Damian Lewis, soon to appear in the West End in Edward Albee's The Goat, or Who is Sylvia?. He is on his lunch break from playing a man who confesses to his wife that he has fallen in love with a goat.

I tell him about Alfred Kinsey.

"Very good," he says with an approving but unemotional nod, as if this were a game of chess. "Are you going to ask me the same question?"

I nod back. He takes a mouthful of salad. Swallows it.

"My research hasn't taken me that far yet," he says. "But."

Another mouthful.

"We have found out some surprising facts."

Ian Rickson is directing this production, which stars Sophie Okonedo as Lewis's stage wife, and the way Rickson likes to work involves inviting various experts to come and talk to the cast. In this first week round the rehearsal table, they've had a classicist tell them about the traditional structure of the play, as well as about bestiality through the ages; and they've heard the psychotherapist Susie Orbach tease out the psychoanalytic strands. In the process, Lewis asserts, they've discovered that "a high - I think surprisingly high - percentage of people have had the fantasy of sex with an animal. Ten per cent."

That's just the fantasy. But, he adds, "we had a woman come in the other day to talk to us, and she said that it still went on - here in this country, isolated farms, men and sheep..."

"What kind of expert was she?" I ask.

"Er, she wasn't an expert," Lewis admits. "She was just a friend of the cast."

Lewis is dressed up - or at least he seems that way to me. He has entered the restaurant wearing a urine-coloured leather coat, pilfered, he says, from a production at the Almeida over a decade ago. He flings it on the seat beside him, revealing several more layers beneath: a blue cotton jacket, a tweedy waistcoat, a button-down shirt and loosened tie. His pale red hair is whooshed back, as if styled in a wind tunnel. The ladies lunching around us turn to look at him and whisper, and despite Lewis's low-key, always affable manner, he hardly appears as if he'd want it any other way.

He explains that it's two years almost to the day since he started rehearsals for his last stage performance - David Mamet's American Buffalo - at the arts centre next door. He and his co-stars John Goodman and Tom Sturridge always had lunch in this restaurant, and they always ordered the same salad, which seems to include most of the ingredients in the kitchen.

"Just a minute," Lewis says, getting out his iPhone. "I have to email a photo of the menu to John and Tom to let them know I'm here."

Intimate endeavours

Lewis is 46. Though often mentioned in the same breath as younger fellow public school-educated actors Eddie Redmayne and Benedict Cumberbatch, his career has been markedly different from theirs. He has predominantly focussed on serious theatre and smart, high-class television, both of which are more intimate endeavours than major Hollywood films.

Lewis's stardom - which began in 2001 with Band of Brothers, the wartime series produced by Steven Spielberg and Tom Hanks, and exploded with Homeland, in which he played Nicholas Brody, the US Marine turned possible Al-Qaeda killer - has brought him into our living rooms, week after week, and left us hanging on the edges of cliffs. He is commanding but ambiguous.

If there is a unifying thread - and this goes some way towards explaining why viewers have loved his many complex roles so much - it's that Lewis trades in heroism, taking stirring ideas about loyalty and showing all the creases in them. Spielberg cast him as Dick Winters because he'd seen him on stage as Laertes in Hamlet, a pained role of double revenge. In Wolf Hall, the series based on Hilary Mantel's prize-winning novels, he turned Henry VIII into a very human sort of king. Now his steely gaze is evolving in Billions, a New York financial thriller in which he plays the slick hedge fund manager Bobby Axelrod.

"He's an emotional actor, but he's thoughtful as well," says Ian Rickson, who suggests Lewis's career will only continue to grow in interesting ways. Remembering his sweaty, tearful performance in the final episode of Homeland's first series, when Brody takes a call from his daughter while a suicide bomb is strapped to his chest, Rickson describes Lewis's acting as "intensely, beautifully, deeply calibrated", and points to "that really dynamic, masculine power he's got, yet he's got a fine touch".

Lewis tells me that he always wants "a job to be serious in some way". He knows he has to be careful not to offend anyone when speaking of the work that sustains him, but that's what he's looking for - and just now, that means the stage.

"I find that theatre, increasingly, has started to attain a spiritual dimension for me in my life," he says. "I do think that theatre, at its best, has a shamanic quality. And I think the collective consciousness is very strong in a theatre. That's because of the moment of shared experience - the moment at which the story is told for the first time that day, or new-minted that night by the cast: as it is spoken it is received by the audience." That isn't true of film, he explains. "So I do find that there is something congregational about theatre." And already, just in rehearsal, he says, "I feel replenished by it."

A 'mind-bending' play

Edward Albee's play, written in 2000, is a transgressive, layered thing: shocking, and perhaps absurd. Yet it explores, by the apparently improbable means of an affair with an animal, universal ideas about love, and tolerance. "It was at that moment that I realised ... that she and I were going to go to bed together," says Lewis's character, Martin. And, to his wife: "I won't go into the specifics of our sex with you!" These lines do not suggest that the "other woman" is a goat. A not-quite-subplot is Martin's relationship with his gay son. The point about the need for acceptance is clear. "We prepare for lessenings," says Stevie, the wife - a beautiful line about the receding tide of life, and yet she could not prepare for this. The goat stands for everything we could not have prepared for.

Rickson has thought a great deal about The Goat's relation to Albee's most famous play, Who's Afraid of Virginia Woolf?, written 40 years earlier. On the surface, they are very different: the earlier play brings us into the middle of a ruin - two ugly marriages, full of pain and falsehood; the later one shows the shock when a perfect marriage crumbles. Yet Rickson suggests that, "looking at a lot of [Albee's] plays, however cruel they are, and however verbally skirmishing, they have to be about love. There's a pattern in Who's Afraid Of Virginia Woolf?, which is to do with longing to be known and loved, and a kind of fury about being seen. There's a paradox there, that goes through the plays."

A New Yorker profile published in 2006, ten years before Albee's death, described his long-standing allegiance both to animals and to feral behaviour in humans. That reaches its summit in The Goat, the stage directions of which include lines such as "A huge animal sound: rage". A parenthesis below the title offers the play as "notes toward a definition of tragedy"; in its form, its content and its "Medea-like ending", as Lewis puts it, The Goat refers to the origins of tragedy itself. The word means "goat song" in Greek, and the sacrifice of a goat was often the climax of Athenian dramatic competitions.

How West End audiences will respond remains to be seen, but it is bold and brilliant to bring such a proposition to a broad audience. Albee's work is, in Lewis's description, a "mind-bending play", and Rickson says he is very moved by the fact that "a writer in his 70s, who had such a variable career, in terms of success and renown, should write perhaps his most radical play, which feels to me really contemporary."

One of the things the play has made Lewis think about is "something that's always uppermost in my mind: how present you are as a father for your kids. And how important it is to be present, and how quickly you feel guilt when you're not present ... Are you not having your chips?"

He reaches for the salt and adds some to my leftovers.

The epiphany

Lewis is married to the actress Helen McCrory; they have two children, aged 10 and nine. As far as anyone can tell, they manage to balance two very successful careers with a relatively sane home life in London. It doesn't always go exactly as planned.

Last year they meant to move to New York as a family, while Lewis made Billions. But McCrory, who had recently performed both Medea and Terence Rattigan's The Deep Blue Sea at the National Theatre, was offered the leading role in Fearless, a six-part ITV drama scripted by one of the writers of Homeland. They all agreed, Lewis says, that she should take it.

"We were trying to work out how we were going to remain: a) together; b) happy; c)...." He drifts off.

"What's c)?" I ask.

"God knows," he says, laughing.

"A) together and b) happy - I think that's enough, for one indiscreet interview."

Lewis ended up taking the children with him to New York, alone.

"I'm not going to pretend that I swanned through it - I felt pretty frazzled by the end of it," he admits. "I think Helen adjusted ... alarmingly well, shall we say, to four months without the kids or me. Never seen her happier, calmer."

In this mid-life moment, he says, he craves sleep, and time to read, and ... "I'd say 'stillness', but I'd be lying," he reflects. "It's a constant duality, isn't it - trying to elasticise time: wanting stillness, but actually being a junkie for the excitement of life." Sometimes, he says, life seems like "a series of incomplete ideas, actions, thoughts...." He laughs. It's like, he says, "you're in a Laurel and Hardy sketch and you didn't get out of the way - Stan turned around with the ladder and you got hit on the head, and then you stood up and it comes and hits you from the other side. I feel that's what life's like."

Lewis doesn't think his epiphany, if it ever comes, "will involve Cupid's arrow and a goat". But you never know.

"I'm a junkie for excitement of life," says Actor Damian Lewis, star of The Goat, or Who is Sylvia?. Provided To China Daily