If you want the sense of truth that comes from an eyewitness account you use the first person. The story is told by the main character from their point of view, and we stay inside the head of someone intimately involved with the events. He can explain his actions and motives. Which is presumably why Lance Armstrong chose not to.
In the Oprah Winfrey interview he refers to himself in the third person: “The leader of the team, the guy that that my team-mates looked up to”. For years he’s been ‘Lance Armstrong’ rather than ‘I’. Referring to himself in the third person lets Lance look back and tell his story, creating distance and suggest that that was then, but this is now. So much has changed he wants us to believe, as he gives himself a keen but not unfriendly stare: “You say you are the winner of seven Tours, a cancer survivor and founder of a charity foundation. Yet you remind me of someone…someone I’ve met before.”
He’d like us to believe he has little to do with his old self, the drug cheat, but that person is still there.
The main limitation to first person narrative is you have to be present in every scene. In telling his story Lance would need to be right there in the middle of the action, a key player, upfront and close to the needles, the bribes and bullying.
But what do you think?