The best cyclists in the world are so good at it because
1. Their bodies excel at removing carbon dioxide from their systems, allowing oxygen to renew supply in muscles that need it the most. This can be increased obviously by blood doping, which adds to your supply of hemoglobin and thus allows you to carry more oxygen to your muscles. However, it is also acquired from intense training of the heart muscle, strengthening of the legs and arm muscles, bla bla bla. The stronger your body is, the better it can deal with the buildup of carbon dioxide and the better it can remove it from your system.
2. Working out doesn't just produce carbon dioxide. When your body runs out of oxygen in key muscles, it begins to respirate anaerobically, which means you are producing lactic acid instead of breaking down pyruvate into smaller molecules and moving it into the Kreb's cycle, which requires oxygen to be completed. Instead, your body has to free its electron receptor groups, and thus the electrons (hydrogens from the breakdown of glucose) are pushed into lactic acid. Lance already had an incredible and superhuman body capable of dealing with this lactic acid buildup - that's what makes cyclists like the pros so much better than me and you. When we would get cramps and have to stop on top of a mountain, these cyclists are barely even getting tired - their bodies are removing the lactic acid just as fast as we can build it up.
When Lance was diagnosed with testicular cancer, he had a large tumor mass growing in his body. Tumors require a HUGE amount of energy to grow - as they are growing with reckless abandon. As a result, they often produce lactic acid - and chemo radiation causes people with tumors to grow increasingly tired as their bodies try to keep up with the tumor's need for energy and increased burning of glucose and conversion to lactic acid. His battle with cancer may very well have turned his already superhuman system of lactic acid removal into quite another beast in itself.
Once again, I'm shocked and appalled by the news and really hope it isn't true. I just wanted to provide another side to the argument. There was a scientific study done on Lance's body and it found a lot of this stuff to be quantifiably true. I'll add the link into my post if I can find it. Cheers.
Edit: Article, not the scientific article I found before because I only had access through my University's library, so I can't link it so you can all see it. I apologize, some google searching may help clear it up a bit.
http://www.ironmanmagazine.com/index.cfm?page=article&go2=1459