Answer by taking a quote from the following article:

Mortimer was born in Hampstead, London, the only child of Kathleen May (nee Smith) and Clifford Mortimer, a barrister who became blind in 1936 when he hit his head on the door frame of a London taxi but still pursued his career. Clifford's loss of sight was not acknowledged openly by the family. John Mortimer was educated at the Dragon School in Oxford and Harrow School, where he joined the Communist Party, forming a one-member cell. Originally Mortimer intended to be an actor (his lead role in the Dragon's 1937 production of Richard II gained glowing reviews in The Draconian) and then a writer, but his father persuaded him against it, advising: "My dear boy, have some consideration for your unfortunate wife...

Mortimer was called to the Bar (Inner Temple) in 1948, at the age of 25. His early career consisted of testamentary and divorce work, but on taking silk in 1966, he began to undertake work in criminal law. His highest profile, though, came from cases relating to claims of obscenity, which, according to Mortimer, were "alleged to be testing the frontiers of tolerance." He has sometimes been incorrectly cited as a member in the Lady Chatterley's Lover obscenity trial defence team, though this is inaccurate. Mortimer did however successfully represent publishers John Calder and Marion Boyars in their 1968 appeal against their conviction for publishing Hubert Selby, Jr.'s Last Exit to Brooklyn. He assumed a similar role three years later, this time unsuccessfully, for Richard Handyside, the English publisher of The Little Red Schoolbook. Mortimer was also defence counsel at the Oz conspiracy trial later in 1971. In 1976, he defended Gay News editor Denis Lemon (Whitehouse v. Lemon) for the publication of James Kirkup's "The Love that Dares to Speak its Name" against charges of blasphemous libel; Lemon was convicted with a suspended prison sentence, later overturned on appeal. His defence of Virgin Records in the 1977 obscenity hearing for their use of the word bollocks in the title of the Sex Pistols album Never Mind the Bollocks, Here's the Sex Pistols, and the manager of the Nottingham branch of the Virgin record shop chain for the record's display in a window and its sale, led to the defendants' being found not guilty. Mortimer retired from the bar in 1984.

Did he win the case?
Lemon was convicted with a suspended prison sentence, later overturned on appeal.