The case could set a precedent for other companies, potentially costing them over £13bn, the FT has reported.
Lloyds Trade Union has described the gap as a "£20bn pensions discrimination time bomb" on its website.
The union wrote: "The outcome is straightforward. The pensions of female members of the pension schemes increase at a lower rate than the pensions of male members.
"That is discriminatory on the grounds of sex, or put another way, women receive less pay than men for doing the same work."
The case will focus on issues around balancing payments made to men and women who were contributing to guaranteed minimum pensions (GMPs) in the 1900s.
GMPs were lower for women because women were to receive their pensions from the age of 60, and men from the age of 65.
The issue will impact over 100,000 women at Lloyds, the trade union said, who are thought to be missing out on £2,000 each - roughly equating to a £300m bill for the bank.
Lloyds Banking Group has been approached for comment.
In 2012, the Department for Work and Pensions said GMP schemes must be equalised - but the industry estimated at the time that the step would cost over £13bn, without taking administrative fees into account.