From the American Airlines website:
Passengers Not Accepted
The following types of passengers will NOT be accepted for travel:
Passengers who must travel on a stretcher.
Pregnant passengers expecting delivery within seven days of departure. For travel trans-atlantic, trans-pacific, and to or from Central or South America, is not permitted if expecting delivery within 30 days of departure.
Newborn babies (within seven days of delivery) unless parent or guardian has a medical certificate indicating travel is authorized.
Customers with questionable contagious diseases. Contact SAC for determination. Queue record to DFW105/11 or contact American Airlines reservations. Contagious diseases are indicated below.
Chicken Pox
Diphtheria
Hepatitis A
Lice
Measles - German and Red
Meningococcal Meningitis
Mumps
Polio
Open, draining or bleeding sores
Tuberculosis (TB)
Comatose passengers are not accepted on American Airlines. The passenger must be able to follow emergency procedures.
Passengers unable to sit upright with seatbelt fastened. The only exception is a passenger in a body cast. Contact American Airlines Reservations for details.
That means active untreated lice. It doesn't say people who already did a RID treatment and a comb through.
I have to fly in a few days. I wonder if I can reserve a lice free seat? 

Still, I'm allowed to have one. I know first hand what a pain in the rear it is to have something happen right beofre your trip and have to cancel or reschedule. We rescheduled when DS came down with pink eye right before a trip. We did have time for him to be on the drops for more than 24 hours before our flight but we had dealt with it twice that school year already and had a hard time getting rid of it so DH and I decided it would be irresponsible to just assume the drops would work fine and travel as planned. I would estimate it cost us around $600 in change fees and lots and lots of frustration to move the trip back but I felt better knowing that when we boarded that plane that no one else was going to come down with pink eye because of my child and our desire to take vacation as planned.