Signs point to no:
In 2008, Jesse Rissman from Stanford University showed that fMRI scans can reveal if volunteers thought they had seen a face before, but not if they had actually done so. If people are convinced of their lies, or if they have simply forgotten crucial information, the scans will not pick that up.
Update from a reader:
It's important to remember that lying requires intent. If one believes something that is factually incorrect and then communicates that falsehood, that isn't lying. Lie detectors may actually be very sensitive to actual lying while completely failing to detect "unintentional falsehood".