A rarity, indeed, to be greeted by a top achiever without having to shoulder past an army of agents tapping a wristwatch and snapping: "You've got five minutes."
A shady nook down by the riverside in Surrey on a sunny morning enhances the pleasurable aspect of the assignment. There Lawler, a hunky, 32-year- old osteopath from Ottershaw, is preparing to paddle his own canoe, as he has been doing with remarkable, if largely un-remarked, results at international level for many years.
Canoeing, you see, never makes a splash headline, but just about every weekend from April through to October those inclined to scour the small print will discover, down among the sport-in-brief, that someone, somewhere, has won a medal for Britain.
Two weeks ago it was again Lawler, whose victory at Gyor in Hungary brought his fifth gold in the World Marathon Championships, and a sixth overall in canoeing, a record which overhauls the five world slalom titles won by the great Richard Fox, now a professional coach in France.
But who outside of the sport has ever heard of Lawler? Or, indeed, of 22-year-old Anna Hemmings, an economics student from Shepperton who completed a unique golden double as the first British woman to become a senior world champion in the same event.
Last weekend there was more success for Britain when Manchester's Paul Radcliffe struck gold in a World Cup slalom at Bratislava in Slovakia, his second such success this season. This weekend sees Scotland's Campbell Walsh among the favourites for a medal in another World Cup event in Germany, and it should be worth turning to the results section next weekend when a strong British team, including Anna Hemmings and her Elmbridge clubmates Ross Sabberton and Paul Darby-Dowman, compete in the World Sprint Championships in Milan.
The Elmbridge club, nestling on the towpath between Weybridge and Walton- on-Thames, is deemed to be the most successful in the world at producing canoe marathoners. At last year's World Championship it registered more medals than any individual nation.
Run by Lawler's family - his father, Roland, is the chief coach - Elmbridge has an honours board dripping with glory in a discipline of the sport which strangely has yet to achieve Olympic status, although Olympic traditions are deep-rooted in the Lawler household, stretching back over the last eight Games.
Ivan Lawler has competed in three Olympic sprint events and Sydney, he says, is likely to be his swansong. An Olympic medal would certainly be the jewel in the clubhouse crown.
One of the problems with canoeing is that it embraces a bewildering and confusing array of disciplines. Sprint and slalom are the recognised Olympic events; next comes the marathon, raced over 26 miles, virtually the same distance as its road-running counterpart and lasting some two-and-a-half hours. There are also white-water racing and novelty events such as canoe polo and canoe sailing.
It is the sprint, the slaloms and the marathon in which the serious business is done, and there cannot be a sport in which Britain has collected more world champions - some 40 in as many years. You could argue that boxing is marginally more prolific, but these days fistic titles are as casually affixed as luggage tags on a package deal to Palma. Because it isn't a punters' pursuit, canoeing achievements tend to be sniffed at. Yet it demands as much time and dedication, as well as physical effort, from its practitioners as from their counterparts in more popular and better publicised pastimes where the rewards are infinitely greater.
Lawler first stepped into a canoe as a five-year-old following the family tradition. Like Hemmings, he also played several other sports but none, he says, brings greater enjoyment than canoeing. "When you read that people do a sport because they enjoy it, it makes it all sound a bit Mickey Mouse," he says. "But you do it because of everything that comes with it, like a bit of self-respect and a bit of pride. It's not just the enjoyment. It becomes what you are. It gives you an identity."
In Hungary, around 50,000 lined the riverbank to watch Lawler and Hemmings do their bit for Britain, beating competitors from Australia, America and the cream of Europe. Here their usual audience is two men and a duck, especially when they slip their kayaks into the Thames around 7am every morning.
They are a special breed, canoe marathoners. A bit like their running counterparts, though Lawler likens their event more to a cycling road race.
"It's a bit like being in the Tour de France. You don't have to go hell- for-leather all the time. You can hide in the pack, in a slipstream, surfing a wave, almost, and then give it a good sprint before hanging back again. It's all about tactics. You try not to collide and you must keep out of trouble."
There are some 24,000 competitive canoeists in Britain and up to one million paddle for pleasure. It is growing quickly but still remains virtually a sponsor-free zone, though the elite competitors now receive Lottery funding. The sprinter Radcliffe, a science graduate now training for the World Championships in Spain, said: "This funding makes all the difference, enabling us to compete on level terms with nations who looked down on us before. Right now we have some of the best canoeing prospects for many years."
This is not a sport where they like to make waves but it is heartening to see that, despite keeping quiet about it, we are beginning to rule them.