The Texan's predecessor as the Tour's dominant figure was Miguel Indurain, who recorded the last of his five successive victories 10 years ago. At the peak of the Basque rider's fame, Spanish television covered almost every bike race available, sponsors fell over themselves and the Tour press room was dominated by Spanish voices.
Today cycling is infrequently broadcast on Spanish television, two of the biggest sponsors, Banesto and ONCE, have withdrawn and newspapers which used to send three reporters to cover the Tour now make do with one.
Yet if cycling across the Atlantic wonders whether there is life after Armstrong, who has become one of the biggest figures in American sport, there can be little doubt that he has raised the profile of bike racing - and the Tour in particular - to unprecedented levels worldwide.
The phenomenon of the all-conquering sports personality has been a feature of the new millennium. The achievements of Armstrong in cycling, Michael Schumacher in motor racing and Tiger Woods in golf, combined with the potential for Roger Federer to build on his current supremacy in tennis, pose questions as to whether such domination is healthy and whether their retirements will leave an unbridgeable gap.
If motor racing is a guide, the end of the Armstrong era will benefit cycling. Formula One has enjoyed a new lease of life this season as Schumacher, seven times world champion, has been left chasing Fernando Alonso and Kimi Raikkonen. Television viewing figures have gone up in most major European countries. The most spectacular rise has been 50 per cent in Spain, thanks to Alonso, but even in Germany the figures are up by two per cent.
Most Germans might prefer to see Schumacher winning, but the return of true competition has has clearly been welcomed. Formula One has had its dominant champions in the past, but they nearly always had fiercely competitive challengers.
Even when McLaren ruled, the rivalry between their two drivers, Ayrton Senna and Alain Prost, provided compelling entertainment. Senna won eight of the 16 races in 1988 and Prost seven; Senna would have won nine had he not collided with Jean-Louis Schlesser while lapping him at Monza two laps from victory.
Yet if Schumacher's demise will be welcomed in many quarters, few will doubt the value of his contribution, least of all Bernie Ecclestone, Formula One's ringmaster.
"People like to see a superstar, and then see who is going to beat him," he said in an interview at the height of the German's domination. "When boxing was at its peak, Muhammad Ali was The One. People were waiting to see who was going to beat him. When Bjorn Borg was at his peak he was unbeatable. But you knew someone would come along and beat him."
In Borg's case that was John McEnroe and it is arguably their rivalry for which both players are now best remembered. Many aficionados would regard Peter Sampras as better than both of them, but the view that often prevailed as he won his seven Wimbledon titles was that the American was "boring".
This, however, was more a reflection of the failure of anyone, despite the best efforts of Tim Henman, to offer a sustained challenge. Conversely, the perennial efforts of Chris Evert used to provide a welcome counter to Martina Navratilova's domination.
Earlier this year there was talk of a "Fab Four" in men's golf, but Ernie Els, Phil Mickelson and Vijay Singh have trailed behind Woods, who took his major titles to 10 with victory in The Open last weekend.
However, it would be hard to argue that the supremacy of Woods, a model champion, is bad for the game. Will we most remember Woods at St Andrews in 2005 or his predecessors as Open champion in 2004 and 2003, Todd Hamilton and Ben Curtis? If the pre-war reign of Joe Davis did little to raise snooker's profile, the domination of Steve Davis and Stephen Hendry built strongly on the sport's rising popularity following the arrival of colour television. Phil Taylor's extraordinary 12 world titles have helped recapture some of the shine which darts lost after Eric Bristow and Jocky Wilson first drew the armchair public's attention.
Are there times, however, when a champion can just become too good? Squash was one of the world's up-and-coming sports, but the utter domination of the men's game by Jahangir Khan in the 1980s did little to build on that popularity. Over a period of five years and more than 500 matches he was simply unbeatable. When Jahangir retired in 1993, Jansher Khan, a distant cousin from a family that ruled for decades, promptly took over.
Despite attempts to make the sport more viewer-friendly, particularly for TV purposes, its appeal has slumped in recent times. Not even the pre-eminence of several home-grown world-class players has been able to arrest that decline in Britain, where there has also been a major fall in the number of participants.
In British rowing, meanwhile, the Olympic achievements of Steve Redgrave and Matthew Pinsent raised interest to new heights, but, despite the presence of several world-class rowers, the sport is struggling to maintain it. Henley Royal Regatta barely made a ripple this year in the British media, which took a keen interest in the sport only when its two most famous oarsmen got back in a boat for a one-off race.
An inescapable conclusion is that a sport must have a basic underlying appeal to sustain an audience's interest. Armstrong, for example, has helped to strengthen interest in cycling in the sport's traditional strongholds, but the appeal to Americans has clearly been his extraordinary personal story of recovery from cancer rather than his sporting exploits.
"Few people in this country cared about bike racing before Lance Armstrong," Jeff Schultz wrote in the Atlanta Journal-Constitution. "Only those same few will care about it after Lance Armstrong."