Suspected psychopaths can be identified through other traits, however if they're sufficiently high-functioning it typically takes a forensic psychologist and a bit of time to resolve. So you have to have both suspicion that someone is a pathological liar and access to a trained person to sort things out. So on the one hand it doesn't make them magically immune to investigation, but it does require different resources than standard police techniques. FBI staff for example do get some training in this area, but you need to have experience interviewing actual psychopaths to prepare you for dealing with them, it's one thing reading about them but quite another experiencing them in person.
(Incidentally, if people think Hannibal Lecter when they hear "psychopath" then think again, although he had some psychopathic traits (grandiose sense of self), he was really just yet another Hollywood-ised mad killer. The character from Wolf of Wall Street is probably the closest Hollywood has come to an accurate portrayal of a psychopath).