It is a myth that chlorine in the pool kills lice. It would be a convenient solution for parents, but no such luck. Chlorine has no effect on lice.
So then, is drowning the lice in swimming pools an option? When your hair gets wet, lice go into a state of “suspended animation”. What does this mean? Well, remember that game you used to play as a kid called “Red Light, Green Light” and when the leader said “red light” you had to immediately freeze and stay that way until he said “green light” or you’d get eliminated? As soon as your head gets wet, lice go into “red light” mode (they freeze) and they can stay that way and hold their breath for several hours! So in order to drown lice, you’d have to keep your head completely under water for more than 2 hours.
There is a silver lining to all this. Even though the pool won’t kill lice if you have it, you also can’t get lice in swimming pools. The live bugs won’t leave someone’s head when it’s wet, since they are in suspended animation. And the nits (eggs) are glued onto the hair with a cement-like substance that is unaffected by water or chlorine.