It features two desk lamps (inspired by a Luxo brand task-light on John Lasseter's desk, hence the title), one larger (implicitly older, named Luxo) than the other. Luxo Jr. plays with a small rubber ball, as Luxo reacts to its antics. Luxo Jr. then accidentally breaks the ball and is admonished by Luxo, after which it finds and plays with an even larger ball.
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