I wouldn't exactly call it intelligent to lie to a court ;) Perhaps another descriptor would be more precise? For that matter, can one be "truly lucid" if one lies in such a manner?
Lucidity is a feeling let's say. And the stuff you feel it "about" does necessarily mean that the stuff is legit.
Or to quote Moby Dick ~ "Human madness is oftentimes a cunning and most feline thing. When you think it fled, it may have but become transfigured into some still subtler form..."
People with schizophrenia are often not lying, they really believe the bizarre things they say. How do you know what your brain is telling you is true?