- Granddaughter of Roy Redgrave
- Children, with John Clark: Ben, Kelly Clark, Annabel Clark.
- Daughter of Michael Redgrave & Rachel Kempson,
- Sister of Corin Redgrave & Vanessa Redgrave
- Aunt of Natasha Richardson, Joely Richardson, Luke Redgrave and Jemma Redgrave.
- Tony award nomination for "Mrs. Warren's Profession" 
- Became a naturalized U.S. citizen.
- Awarded an OBE, or Officer of the Order of British Empire, by Queen Elizabeth II in the New Year's Eve Honors List 2001.
- Both she and her sister, Vanessa Redgrave, were nominated for the 1966 Best Actress Academy Award. Lynn was nominated for Georgy Girl (1966), and Vanessa was nominated for Morgan: A Suitable Case for Treatment (1966). They both lost out to Elizabeth Taylor, who won for Who's Afraid of Virginia Woolf? (1966).
- Aunt of Carlo Gabriel Nero
- Was one of the judges in the 1972 Miss Universe pageant.
- Has twice been nominated for Broadway's Tony Award as Best Actress (Play): in 1976 for George Bernard Shaw's "Mrs. Warren's Profession;" and seventeen years later, in 1993, for "Shakespeare for My Father," her one-woman show about her relationship with her father, Michael Redgrave.
- Won the 2004 Barrymore Award (honoring Philadelphia theater) for Outstanding Leading Actress in a Play for "Collected Stories."
- Played "Final Interview Subject" in Kinsey (2004) as well as "The Queen" in Everything You Always Wanted to Know About Sex * But Were Afraid to Ask (1972), which was inspired by the sex manual by Dr. David Reuben, Everything You Always Wanted to Know About Sex (But Were Afraid to Ask) (1969), three years after the Masters & Johnson study Human Sexual Response.
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