The increase from the current level of 28% is among a series of commitments being made by chief executive Antonio Horta-Osorio. The move comes after Deputy First Minister Nicola Sturgeon proposed that the SNP, if given responsibility for equalities, would set a mandatory target of 40% of board targets being occupied by women.
Last week, the Scottish Government confirmed it has accepted an invitation from Jo Swinson, the UK Government's Minister for Women and Equalities, to present "detailed proposals" for setting a legally binding quota for the number of women on the boards of devolved public bodies.
Ministers agreed to draw up plans for increasing the number of women in top jobs after calling for extra powers from Westminster.
Mr Horta-Osorio, who will unveil the bank's Helping Britain Prosper Plan in a speech tomorrow, said the commitment is an important step in regaining trust in the banking industry.
The group's plans also include a pledge to boost net lending to small and medium-sized business by more than £1 billion this year and the support of more than 80,000 first-time buyers, up from last year's target of 60,000.
It comes a few weeks after the bank was fined a record £28 million over incentive schemes that rewarded staff with "champagne bonuses" and put advisers under pressure to hit sales targets or face demotion.
The group, which was rescued by the taxpayer during the financial crisis after swallowing up Halifax Bank of Scotland, remains 33% state-owned.
Mr Horta-Osorio said: "The reputational impact of the financial crisis upon the banking industry's stature has been immense.
"Rebuilding a sound reputation founded on the highest standards of responsible behaviour is key to the industry's long-term success. But words alone are not enough to change public perception and regain trust. We must be able to provide meaningful commitments and allow ourselves to be independently measured against those."
Vince Cable, the Secretary of State for Business, welcomed the move by Lloyds, saying businesses have a duty to push for change in equality issues. He said: "Despite good progress since 2010, we are still not tapping into the talents of half the workforce.
"Too few women occupy the top positions of our companies today. Yet the evidence is clear - those businesses with diverse senior management make better decisions and that is reflected on the bottom line.
"This is not about political correctness, this is about good and profitable business sense. As a government we have resisted binding quotas for women executives, so business-led moves such as that by Lloyds today is crucial to show leadership and change on this important agenda. We need to make sure that becomes standard practice in the UK."
Last week, the Deputy First Minister said increasing the number of women in Scotland's boardrooms would be a "gain of independence".
She told a conference if Scots voted Yes in the referendum, an SNP Government would apply positive discrimation legislation to private companies as well as public bodies.
At present, the Scottish Government is only seeking powers to ensure 40% of appointments to public boards are women.
A Scottish Government spokesman said: "Scotland's Future makes clear the importance and value of an increased participation by women in Scotland's economy and includes our aspiration to see at least 40% of places on public boards filled by women and plans to significantly increase funded childcare.
"This is not simply the right thing to do, it will provide women with much greater opportunity to work and develop their careers, in turn boosting our economy and ultimately benefit us all."
The commitments by Lloyds will be independently monitored and reviewed every year. Further information about the targets will be announced on March 6, when it publishes its annual report.