Harrow was born in Auckland and attended Auckland University. She graduated from RADA in 1968, and joined the BBC Radio's Repertory Company.

Her stage career started at the Royal Shakespeare Company; roles there included Olivia in John Barton's production of Twelfth Night opposite Judi Dench, and Portia in The Merchant of Venice opposite Patrick Stewart. Other leading roles in the UK theatre include Juliet opposite John Hurt's Romeo at the Belgrade Theatre in Coventry, and Ann Whitfield in Man and Superman opposite Peter O'Toole at the Theatre Royal, Haymarket.

Harrow has performed on stage all over America. She took over the central role of Vivian Bearing in the Pulitzer Prize winning play 'Wit' in its long-running off-Broadway production in New York. She was named 2001 Performer of the Year in Pittsburgh for Medea. Other roles include: Raynevskya in The Cherry Orchard at Yale Rep and the Chautauqua Theatre Company, where she also played Kate Keller in All My Sons. She played Creusa in the Washington Shakespeare Theatre Company's 3/10/2009–4/12/2009 production of Euripides's Ion.

She is known for playing Nancy Astor, the first woman elected to the Parliament of Great Britain, in the 1982 BBC drama of the same name; it aired on PBSs series Masterpiece Theatre in the United States. Harrow played journalist Kate Reynolds in The Final Conflict (1981) and Lizzie Dickinson in Lizzie's Pictures (1987), BBC. She won the Australian Film Institute Award for Best Actress in a Leading Role for her performance in The Last Days of Chez Nous. Her last TV performance to date was as Lizzie Kananaugh in the series Kavanagh QC starring John Thaw. She left the series in order to move to America.

She had a relationship with actor Sam Neill. Their son Tim was born in 1983.

She is now married to whale biologist Roger Payne, and lives in Vermont. Roger is founder and President of Ocean Alliance. He and Scott McVay discovered the long, complex and apparently random sounds produced by male humpback whales are actually rhythmic, repeated sequences, and therefore, are properly called 'Whale songs'. Lisa and Roger have created a lecture/performance piece called 'SeaChange: Reversing the Tide' .

Harrow is the author of the environmental handbook What Can I Do?, published in separate editions for Australia, New Zealand, the UK and the US. She has a website to promote the book.. The U.S. edition:

• (pbk. : alk. paper) Includes bibliographical references.