According to its Q3 results today, it has already paid out £3.7bn and said it expected this to rise to £5.3bn.
These figures led to a statutory pre-tax loss for the firm of £583m for the first nine months of 2012.
Lloyds said while claims had dropped compared to Q2, they were still higher than it had forecast earlier this year.
Lloyds was the biggest provider of PPI and accounted for a third of the market. It said it hoped to have a clearer idea of the ultimate cost of PPI by its full-year results in March 2013.

Costs for Project Verde were £399m in the first nine months of 2012 and have cost £611m so far. Project Verde is the title given to the disposal of 632 branches to the Co-operative Bank.
It said it was the first bank to access the new Funding for Lending scheme with lending commitments to small and medium sized enterprises increased to £13bn and a £500m commitment made to the first-time buyer market.
Group chief executive Antonio Horta-Osorio said: "We have a strong commitment to helping Britain prosper and our early participation in the Funding for Lending scheme is enabling us to extend further financing to businesses and customers in the UK.
"We are confident that, by delivering our strategy to be a simple, customer-focused UK retail and commercial bank, we can rebuild the trust of our customers and other stakeholders and can deliver sustainable returns for our shareholders over time."