I am not sure, but I believe the drone would have to be massive (also, with a massive price tag), compared to current designs.  This drone will needs to carry multiple solid state laser modules, plus a power source that is considerable to power a laser that can shoot down ballistic missiles at a much greater range than those being designed for air to air engagement.  When you add up all the equipment on board, it will probably be really expensive.  So, how many will you also need to provide 24/7  coverage?  Then, if one of these crashes, it will likely be in the price range of a F-22 going down.  Hopefully, the NK will not be capable of shooting one down, given that it will loiter at high altitude, but they might try, seeing this as an act of war.