I agree that Lance Armstrong has had some fantastic results in his cycling career. I would choose Beryl Burton or Reg Harris if I had to stick to cycling - showing my age I know.
There have been extraordinary athletes in lots of sports, but for me the best ever athlete has to be Paul Elvström who won his first olympic gold medal in 1948 at the age of 20, sailing a Firefly singlehanded in Torbay. He went on winning major events up to the 1960s with 2 world championships in 1966.
Paul was an expert in racing single handed dinghies and dominated the Finn class in the 1950s, partly through his physical fitness. He published a guide to the racing rules which was the bible for most racing sailors for a long time.
Racing a dinghy singlehanded is a lot like cycling in the rain - cold, wet, a head wind most of the time and a pain barrier to overcome for top performance. Winning requires stamina, physical fitness and coordination, mental strength, knowledge of the racing rules, endless practice and belief in the god given right to be first over the line.