Lance Armstrong has been a competitive athlete since his teens.
Even if his most celebrated victories have been cancelled due to his extensive use of unallowed performance enhancing drugs, he's bound to have some victories from before the doping era that would still "count".
But unless Lance himself has kept a competition log for all these years, I think tracking down the exact number of wins would be quite difficult.
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He has actually never won a race. This is because despite finishing first he has been disqualified from all his races.
People who take drugs to succeed as athletes are not proper contestants, they are, to most decent people, dishonorable unsportsmanlike cheats.