You can find the answer to this towards the end of Chapter 18. We are not explicitly told that they girl who comes down out of the helicopter is Lenina, but it is certainly implied.
What John does when he sees the girl is to attack her with the whip. He starts calling her various words that all mean something like "whore" and he starts whipping her. He is doing this because he blames her for tempting him.
After a while, his whipping her turns into an orgy that he takes part in. This is why he kills himself.
Actually the reason he kills him self according to my teacher and Aldous huxley is that it's a result of insanity created by the fundamental conflict between his values and the reality of the world around him!