That's what courts and juries are for. Just as the government cannot require that peoples mouths be taped shut, for fear they might shout fire in theater when there is no fire, you can not impose "prior restraint". But once the lie is told, then there can be accusations, criminal or civil. At that point, it's up to the jury.
So, your ability to lie is protected by the first amendment, but actaully lying is not.
That’s not the law.
You are free to lie; not free to defraud.
The question here is whether stolen valor is “speech” and, if so, fraud.