From Lahore using motorway (and staying at road side hotels for 5-10 minutes and filling up for gas after every 100 km or so), it will take 12 hours for anyone to reach Naran.
Leave at 6 am maximum and you will reach Naran at 6 pm definitely.
However I have only counted 30 minutes for the "stuck in Traffic" which basically happens in Abbotabad. But locals tell me that people are stuck here in traffic for 3 to 5 hours also.
So you have to reach Abbotabad at such a time that there is less traffic over there