While he did do a number on cycling, making it loose one of its hero's and all, cycling is a sport that has been around too long for a scandal to completely destroy it. I know that it will be a little while before people care about the Tour de France as much but that does not mean it won't get back there.
The interest in racing, at least where I reside in the United States is not very strong. It appears to have always been a niche sport. For notable races like the Tour De France, there is dedicated television coverage on the former Outdoor Life Network. Outside of the major races, you never really hear about cycling. If anything, all the of the coverage of the Lance Armstrong situation might encourage more people to tune in.
One guy never kills any sport. Not correcting the doping would have killed it. Baseball has survived doping so will cycling. Losing Lance Armstrong will hurt not doubt but it will not end the sport by and exaggeration if anything knowing its clean and no one not even the brightest star is free of the rules will boost the sports legitimize.
I do not think cycling will recover after Lance Armstrong's admission. He was the sport's biggest name and now that he is banned, people will not be watching like they used to. I also think the sport will continue to be dirty even after Armstrong is not part of it anymore.