That's not because he's sick. After all, Armstrong last week won his record six straight Tour de France, a race that has been called the most grueling physical test in all of sports.
No, it's because Armstrong, ever since winning his own life-and-death battle with cancer, has made it something of a mission to show others with the disease that they too can win.
The lanky American was in Prague today doing just that. At a news conference at the city's Motol hospital, where he met with young people with cancer, Armstrong said: "It's still hard for me to go to the hospital because I still have fresh memories of my times in hospitals and I understand what the patients and the families are going through. But as a cancer survivor, I think it's my obligation to share my story and to hopefully provide some hope for a young patient, for an old patient, for a family member, for a doctor, for a nurse. Because let's not forget, the doctors also need to be reminded that there's hope."
Armstrong was diagnosed with cancer in October 1996. He was then 25 years old and although considered a promising rider, few would have imagined him capable of becoming the greatest cyclist of his generation.
And yet that's what he did -- although, even more remarkably, only after winning an epic battle to defeat a cancer that had spread to his abdomen, lungs, and brain.
His doctors initially gave him a 50 percent chance of surviving. They later admitted his chances were less, but had hid the magnitude of his illness in order to give the American hope.
For most people, surviving such an illness would have been victory enough. But not for Armstrong.
Determined like few others, the Texan refused to follow the traditional chemotherapy, which would have ruined his chances of resuming his cycling career as it can greatly reduce lung capacity. Instead, he chose a more severe therapy that was less likely to damage his lungs.
His doctors credited his fierce determination for helping him to recover. Amazingly, Armstrong today said the disease had been "a good thing" for him.
"I think the illness was a wake-up call for me and reminded me that we only have one opportunity in life and in sport," Armstrong said. "And so, in that sense, it was a good thing for me."
Where he rides from here is anybody's guess. There has been speculation that he may not ride the Tour again and instead seek to win races he has excluded in his mission to win the Tour, such as the Giro d'Italia or Vuelta de Espana.
He said today that his calendar for next year is still open, suggesting he may in fact try his luck in Italy or Spain. Some have criticized the American for focusing all his energies on the Tour de France and not riding in more races. Because of that, most experts rank Eddie Merckx ahead of him as the greatest cyclist ever, even if the great Belgian rider "only" won the Tour five times.
At 32, Armstrong knows his cycling days are numbered. He has yet to fix his calendar for next year, but says he will return to the Tour at least one more time.
Can he possibly win it again?
"I don't know. I 'm not a young rider anymore, so obviously my time is limited. I suspect maybe one more [Tour de France victory] -- if things go well," Armstrong said.