The slowness and disorganization are characteristics of ADHD. Have you looked into an evaluation? My DD (third grade) has ADHD and has that characteristic of lying for no apparent reason or just making things up (and she somehow spins things so that they are very believable--reminds me of a sociopath). She also does very impulsive things (like draw on the walls or break things) and then lies about it. She is "almost" normal on medication-- there is a big difference between meds and no meds.
Does the school have a psychologist or a behavior specialist? In your shoes I would either have an independent psychological evaluation, or request that the school do a comprehensive evaluation. Put your request in writing. It sounds to me like there is more going on than just being gifted.
