The company said it will waive the commission Lloyds as the issuing company would normally be obliged to pay a firm running a share sale on it behalf.
With the petition having exceeded 10,000 signatures the government is required to respond. Should 100,000 signatures be obtained, the issue must be considered for parliamentary debate.
Some 374,000 people have registered their interest in the Lloyds Banking Group shares through Hargreaves Lansdown, the company said.
Hargreaves Lansdown noted that further sales of the taxpayer stake in Lloyds are still being made to City institutions.
Hargreaves Lansdown CEO Ian Gorham said: "It's easy to see why so many people are unhappy with the decision to cut out the retail investor. The taxpayer owned stake in Lloyds is being sold to City institutions when the man in the street has to pay full price. We urge the government to rethink. Money from taxpaying working people bailed out Lloyds Plc and they should be given the opportunity to participate in its sale. This share sale is an ideal opportunity for the government to encourage people to invest in their future.”