I wouldn't say that "Tragic Hero" is the best title for him, but he fits the definition. "Posterboy for Doping Era of Cycling" fits better, but that wasn't the question. Lance Armstrong helped a lot of people see potential in themselves they might not have otherwise. That's true despite the fact that he's a compulsive liar, egomaniac, and all-around horrible person. That is the definition of a tragic hero.
By definition, Lance Armstrong is a tragic hero, due to his inspiration in spite of his recent loss of many things that he had earned in life. Even though many believe that the evidence of his doping is solid, his inspiration, albeit an inspiration that was partially built upon corruption, has motivated many to persevere in life.
The title of hero of any kind for Lance Armstrong would be unjust. There is no way one could classify Lance Armstrong as a hero whether it be "tragic hero" or other. He is undeserving of any thoughts even being given to the subject. I say move ahead and let others learn from this huge mistake and not to even concern ourselves with trying to justify Lance Armstrong's actions by labeling him a hero of any kind.
The label of tragic hero does not belong to Lance Armstrong because he was not a hero. Armstrong was a phony and was never a true hero. Armstrong lied to millions of people and ruined lives of many. There are people that are former friends of Lance that hate him. That is no hero.