During his marriage to Cynthia, Lennon's first son Julian was born at the same time that his commitments with the Beatles were intensifying at the height of Beatlemania. Lennon was touring with the Beatles when Julian was born on 8 April 1963. Julian's birth, like his mother Cynthia's marriage to Lennon, was kept secret because Epstein was convinced that public knowledge of such things would threaten the Beatles' commercial success. Julian recalled that as a small child in Weybridge some four years later, "I was trundled home from school and came walking up with one of my watercolour paintings. It was just a bunch of stars and this blonde girl I knew at school. And Dad said, 'What's this?' I said, 'It's Lucy in the sky with diamonds.'" Lennon used it as the title of a Beatles song, and though it was later reported to have been derived from the initials LSD, Lennon insisted, "It's not an acid song." McCartney corroborated Lennon's explanation that Julian innocently came up with the name. Lennon was distant from Julian, who felt closer to McCartney than to his father. During a car journey to visit Cynthia and Julian during Lennon's divorce, McCartney composed a song, "Hey Jules", to comfort him. It would evolve into the Beatles song "Hey Jude". Lennon later said, "That's his best song. It started off as a song about my son Julian ... he turned it into 'Hey Jude'. I always thought it was about me and Yoko but he said it wasn't."  Lennon's relationship with Julian was already strained, and after Lennon and Ono moved to Manhattan in 1971, Julian would not see his father again until 1973. With Pang's encouragement, arrangements were made for Julian (and his mother) to visit Lennon in Los Angeles, where they went to Disneyland. Julian started to see his father regularly, and Lennon gave him a drumming part on a Walls and Bridges track. He bought Julian a Gibson Les Paul guitar and other instruments, and encouraged his interest in music by demonstrating guitar chord techniques. Julian recalls that he and his father "got on a great deal better" during the time he spent in New York: "We had a lot of fun, laughed a lot and had a great time in general."  In a Playboy interview with David Sheff shortly before his death, Lennon said, "Sean was a planned child, and therein lies the difference. I don't love Julian any less as a child. He's still my son, whether he came from a bottle of whiskey or because they didn't have pills in those days. He's here, he belongs to me, and he always will." He said he was trying to re-establish a connection with the then 17-year-old, and confidently predicted, "Julian and I will have a relationship in the future." After his death it was revealed that he had left Julian very little in his will.

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