What family revelation does Lynn share with Abigail? What is Lynn's purpose in sharing it ?

Lynn tells Abigail that she knows Abigail is having an affair, but Abigail won't open up or admit it. The revelation Lynn shares was that her husband had an long term affair;

"Your father had a long-term affair in New Hampshire. Her first initial was F and I never knew what it stood for. I found a thousand options for it over the years."

She shared this information hoping her daughter would share hers.