I am going to say no, there is no rigorous definition.
At first glance I would say yes, a .357 or .44 mag lever action carbine is a PCC.
But then I remember, purists have a fairly strict definition of what a 'pistol' is. A pistol is a handgun that is not a revolver. This is why we have ranges with names like 'Anytown Pistol & Revolver Club'.
Thus an argument could be made that a .357 or .44 mag lever action is actually an RCC: Revolver Calibre Carbine.
Obviously if you are one of those people who think the words pistol and handgun are synonyms, this argument holds no water.