IF Mark Thomson, outgoing director of Edinburgh's Royal Lyceum Theatre, shares in the theatre profession's much-vaunted tendency to superstition, he has a funny of way of showing it. He has decided to take his leave of the illustrious company in this, its 50th year, caring not a jot that he will be departing after 13 years at the helm.

In fact, when I meet him in the upstairs bar of the grand playhouse, in the midst of rehearsals for his final directorial offering (the world premiere of Chris Hannan's new version of the Ancient Greek epic The Iliad), he is in neither a superstitious nor a reflective mood. Rather, he is bristling with creative energy.

Now, he tells me, is as good a time to go as any. "You could go on forever, couldn't you?" he asks rhetorically. "I'm happy because I'm leaving feeling incredibly positive about the company and the work.

"I'm not leaving having wheezed myself through two years in which I didn't really have the appetite. I'm leaving without any bitterness. I feel like I've come to a natural end."

To say that his last two seasons have not wheezed to a stop is a massive understatement. In fact, by general critical acclaim, his final couple of seasons have seen Thomson at his directorial best.

The Lyceum received no fewer than six of the 10 gongs at last year's Critics' Awards for Theatre in Scotland. Thomson himself picked up the Best Director award for his brilliant production of Brecht's The Caucasian Chalk Circle.

If the 2014-15 season brought the Lyceum bouquets aplenty, the current programme has also had the critics reaching for their superlatives. Thomson's superb staging last autumn of Beckett's Waiting For Godot, which boasted a stellar cast including Brian Cox and Bill Paterson, has come in for particular, and richly deserved, praise.

Despite such successes, the director won't be drawn on which of his Lyceum productions give him the greatest sense of satisfaction. "For every one I don't mention, I can hear boos coming from the wings," he says. "I really can't pick out particular highlights, that's for other people to say."

Indeed, Thomson can look back with pride on his entire career thus far. A son of Harthill, North Lanarkshire, he came to the Lyceum following five successful years as director of the Brunton Theatre Company in Musselburgh.

His career has also included playwriting. Highlights include a strong adaptation of James Hogg's classic novel Confessions Of A Justified Sinner, the fine, socially engaged comedy A Madman Sings To The Moon and Pleasure And Pain, an excellent piece based on the writings of the great French writer Maupassant.

Thomson has always had an eclectic artistic taste, and he has carried that forward during his time at the Lyceum. "Being artistic director of the Lyceum has been such a joy because I've been able to put on such a diverse array of work," he says.

"Crazy productions of Faust and The Caucasian Chalk Circle; a wonderful set of Arthur Miller's, directed by John Dove; a beautiful Laurel And Hardy; plays by Moliere and Goldoni; new work by people like Daniel Jackson and Jo Clifford. I feel quite good about the balance and the risk in the programming."

The productions may have been varied, but, successful or not, they have all, he says, been his children. "Even the children that have behaved badly, or become serial killers, or have stolen from banks, or have let everybody down in a really bad way, they've all been loved into being.

"That's all I can do. I introduce a piece of work to the stage with integrity, and I hope that it will flourish. If it doesn't, that's art. If certain things aren't failing every now and then, you have to wonder to what extent there is adventure."

This belief in risk-taking and the right of the artist to fail lies, perhaps, at the centre of Thomson's success at a theatre that is often perceived as being somewhat conservative. The Lyceum, an exquisite, Victorian building in the very heart of Edinburgh, a stone's throw from the city's financial quarter, tends to be compared unfavourably with Glasgow's Citizens Theatre.

The Citz, they say, is the Lyceum's unruly cousin. Living, defiantly, in the ever-changing working-class community of the Gorbals, the Glasgow playhouse is a more dangerous, sexier proposition than the Lyceum, which sits, serenely, like a grand old lady, in the shadow of Edinburgh Castle.

It's a perception that Thomson has always felt keenly. "The Citizens is like going down a Paris side street," he observes. "There's a beautiful, ornate purple light with, 'boys and girls available', and somebody's standing under it with their dress hitched up above their knee saying, 'Come in, I'll show you a good time'."

This observation dovetails with the great Citz director Giles Havergal's comparison of himself with the madame of a brothel. It's a picture that contrasts with the popular perception of the Edinburgh theatre.

"The Lyceum, because of where it is, feels a bit like a grand dame", Thomson admits. "She's saying, 'If you'd like to come in and sit down to some tea, I've got the scones coming shortly.' It's much easier to like the Paris side street. It looks like fun. However, that perception is only to do with external factors, it has nothing to do with the work. The work is just as subversive on the Lyceum stage as on the Citz stage."

Which brings us neatly to the Lyceum's much-fabled audience. Generally perceived to be comparatively well off and, on average, somewhat older than the population at large, they are charged with having conservative tastes.

Thomson, who has watched the theatre's clientele embrace such high modernists as Pirandello, Brecht and Beckett, is having none of it. "They may well be 60 or 70 years old," he says, "but they were doing stuff in the 1960s that you and I never got close to. They were around when rock 'n' roll, free love and drugs were being enjoyed and exploited. They've been exposed to much more dangerous and fluid times than we have.

"They may well live in Morningside now, but maybe they were on the fields of Woodstock taking things they should never have been taking."

The director's description of the radical streak in both the Lyceum company and its audience will make sense to many people who know the theatre. In particular, one suspects, it will be recognised by Thomson's successor, internationally acclaimed playwright David Greig.

Any regret Thomson feels at departing the Lyceum must be tempered, I suggest, with satisfaction that Greig sees in the theatre a legacy that he can build upon. "Absolutely," the director agrees.

"I thought, 'He doesn't need this, so he must want it'. He's taken bloody Charlie And The Chocolate Factory to New York, he's launched The Lorax at the Old Vic [in London]. He's an established artist."

Greig may be about to write the next chapter in the Lyceum story, but Thomson is not quite finished yet. There's still the little matter of his 27th Lyceum production, Hannan's Iliad, to attend to.

"The Iliad is the first piece of Western literature," he comments. "What you're seeing is a culture trying to figure out things that have never been figured out before. For example, what do we feel about war? What do we feel about love? What does betrayal mean? What does torturing a dead man mean? What does the body politic think of a truce?"

Thomson is certain that Hannan is the right modern Scottish writer to take this great work on. "Chris might be embarrassed that I'm saying this, but he kind of writes like Shakespeare.

"He uses apposition and alliteration. In amongst a very speakable dialogue, he's using words in a way that the Jacobeans did. His language is very visceral, very felt, very sensual."

All the things, in other words, that an adaptation of Homeric poetry for the 21st-century stage should be. All of the things, indeed, that one would expect of the final production of a director whose tenure at the Lyceum has been characterised, like the man himself, by a generosity of spirit and an ambitious artistic sensibility.

The Iliad is at the Lyceum, April 20 to May 14. Details: lyceum.org.uk