Nuclear Man takes Lacy into space. Superman then moves the moon in front of the Sun and causes Nuclear Man to become powerless. Superman takes Lacy back to Earth and then takes Nuclear Man and puts him in a nuclear reactor, killing him. Superman says that if people want peace bad enough, the governments of the world will give it to them. Superman then sends Lenny to a boys reform schools and sent Lex back to the labor camp.
Trivia: Near the end of the film, Superman gives a press conference in front of a bluish mirror-glass building which is meant to be the Daily Planet skyscraper in Metropolis (which we all know is New York, sort of). The shot is framed so you can only see the bottom of the building - necessary as it is only about 3 floors high, and is in fact the railway station in Milton keynes, England, about 400 yards from where I work. Even the crowd have a vaguely British look about them - presumably passers-by were recruited and stood there in their own clothes (this would matter less now - Brits look more American than they did in the Eighties).