From the Sparks ruling in the lawsuit brought by Armstrong against USADA earlier this week:
The Court agrees with the reasoning of Slaney and Harding, that federal courts should not interfere with an amateur sports organization's disciplinary procedures unless the organization shows wanton disregard for its rules, to the immediate and irreparable harm of a plaintiff, where the plaintiff has no other available remedy. To hold otherwise would be to turn federal judges into referees for a game in which they have no place, and about which they know little. . .
Armstrong's challenges to USADA's jurisdiction, and his arguments about which rules govern, can and should be made in arbitration. If the panel's resolution of those issues is manifestly unjust and devoid of any reasonable legal basis, Armstrong may have a judicial remedy; but this Court cannot act on the basis of a hypothetical injury.In principle, Armstrong could have won in arbitration, and by choosing not to go through that process Armstrong eliminates the possibility of arguing that the arbitration process was "manifestly unjust" in his case. To make such an argument now he'd have to allege that past arbitration decisions lead to such a conclusion -- not at all an easy case to make.
I say above that the door is not completely closed because in the US judicial system lawsuits are frequently brought from a losing position. However, I'd venture that if Armstrong's fight on this issue is to continue, it will be through CAS and via a proxy, such as UCI.
Of course, another alternative is that this really is the end.
Note: For a largely sympathetic analysis of the content of the dispute see here (which is the source of the image above) and for an unsympathetic view see here.