Lance Armstrong admitting that he used drugs while cycling most definitely hurts Livestrong. The bard is tainted now. There was always a positive association with it and now that is gone. The company was built off cheating and people will not want to be associated with it anymore. I've already seen people throwing away Livestrong wristbands
Livestrong will undoubtedly be hurt by Lance Armstrong's admission of doping. People know now that he did cheat and that he did deceive millions of people. The effect, at least initially, will be detrimental to Livestrong. Over time, as people beging to heal, people will remember that what he did for Livestrong was a good and maybe there will be a recovery.
Livestrong basically was Lance Armstrong. If Lance Armstrong was not associated with the foundation, they would not be anywhere near as well-known as they are today. Now that Lance Armstrong has tarnished his name by doping and ruining the careers of other riders, the foundation that many people associate with Armstrong will suffer as well.
Lance Armstrong was a cheater. He doped and lied about it for decades. However, what he did with his Livestrong foundation transcended his sport and offered hope to millions of people. That will not change. Whatever tarnishing happened to Armstrong's reputation, the facts are that his foundation has continued to help those suffering.