Lynn has been nominated for two SAG Awards. In 1999 she was nominated for Outstanding Performance by a Female Actor in a Supporting Role for Gods and Monsters. In 1997 she was nominated for Outstanding Performance by a Cast for Shine.
Lynn has been nominated for four Golden Globes. In 1967 she was nominated for both Most Promising Newcomer-Female and Best Motion Picture Actress-Musical/Comedy for Georgy Girl. She won Best Actress. In 1981 she was nominated for Best Performance by an Actress in a TV-Series - Musical/Comedy for House Calls. In 1999 she won the Golden Globe for Best Performance by an Actress in a Supporting Role in a Motion Picture for Gods and Monsters.
Lynn was nominated for a Tony Award for Best Performance by a Leading Actress in a Musical in 2006 for her performance in The Constant Wife.
Lynn is the sister of Vanessa Redgrave.
Lynn: Looking at my horrible ugly bulk on a huge screen was the turning point in my life.