In George Orwell's 1984, protagonist Winston is repressed by The Party and is unable to realize his ambitions in reality. To cope, he has vivid dreams about his emotions and yearnings. He dreams about his mother and sister, about an idyllic golden country, and about a dark-haired girl.
Jacques Lacan was an influential psychiatrist and self-proclaimed Freudian, although his theories have their own distinct following. His theories on dreams differ from Freud's in that he believed the unconscious to be a language-structured component of the mind, equal in complexity to the conscious; dreams, therefore, are the language-constructs of the unconscious making themselves known to the conscious.
To use Lacan's theories on Winston's dreams, you should show how his repression created the language of his unconscious. His dreams uniformly show selfish tendencies and a strive for individualism; these attributes are dampened by The Party and so can only be fostered in his unconscious. According to Lacan, this is because the unconscious is as purposeful and opinionated as the conscious, and so creates dreams to express its own desires, whether they agree with the conscious or not. Winston's dreams show that his unconscious is powerful in his mind, and able to directly express his desire to be free, despite his devotion to The Party. However, his dreams about his mother show a cruel side of his unconscious that would cast aside even family members to realize his own desires; the unconscious therefore is almost entirely separated from his conscious in need, but echoes his inner thoughts to a higher level.