The chairman of the WestConnex Delivery Authority, Tony Shepherd, is threatening to sue journalist and activist Wendy Bacon over a tweet.

Lawyers for Mr Shepherd, who is also a former head of the Business Council of Australia and chaired Tony Abbott's Commission of Audit, wrote to Bacon last week demanding a correction to her tweet, which she sent on Friday, February 13.

Tony Shepherd, head of the WestConnex Delivery Authority. Credit:Arsineh Houspian

The tweet, which was retweeted three times, referred to Mr Shepherd's role as chair of the consortium that won the Lane Cove Tunnel project.

Traffic forecasters working on the Lane Cove Tunnel, built between 2004 and 2007, massively overestimated the number of cars using the road.