Yours is a theoretical question whereas Avvo is really for people who need some guidance for their personal or business problems.
That being said, He is not being sued for breach of contract but other continuing offenses. Good news: he will have the best lawyers the private sector can provide.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Is this Lance Armstrong posting anonymously?
These are good arguments, but likely will not apply to your situation.
Theoretically, the reason the statute of limitations has not run is because you denied you were using performance enhancing drugs all this time until just recently. Your recent admission could start the statute of limitations on a whole host of claims.
On the other hand, Lance, you can argue that, given all the allegations regarding your use of steroids for the past decade, the government reasonably should have suspected long ago that you were doping.