It is reasonable that people with contagious infections/infestations are not permitted to fly. It is not the airline's fault that this young boy picked up an infection. Unfortunately, head lice are very easy to get. My kids have been infected numerous times, it's a problem because too many people are in denial and far too often schools and such like will not take any action. In this case Delta did the right thing but may have been a bit heavy handed in dealing with it. There is a good chance that a pharmacy in the terminal at Minneapolis would have a concoction that would fix the problem allowing the family to continue. Insisting on a letter from a medic to confirm the lad was bug free was probably over the top. Besides, his parents would have wanted the critters out ASAP.
The place where the father was wrong was insisting the airline should have a specific lice policy. None is needed. A general policy and common sense should be good enough. Or am I just a bit naive?