This resulted in up to 140,000 customers of Lloyds TSB, Lloyds TSB Scotland and Bank of Scotland receiving delayed payments.
Lloyds was the biggest supplier of PPI, accounting for a third of the market.
Lloyds was expected to make redress payments within 28 days but around 87,000 people had to wait over 45 days, 56,000 over 60 days, 29,000 over 90 days and 8,800 over six months.
Other failures included problems with the telephone service which meant customers were not informed of the delay, staff did not have the necessary knowledge and failure to monitor which payments were being made.
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Tracey McDermott, FSA director of enforcement and financial crime, said: "The industry let customers down badly in relation to the sale of PPI. The significant volume of complaints is a product of LBG's own failing and the least customers can expect is that redress, when it is due, is paid prompltly.
"LBG's PPI redress payment systems fell well below the standard the FSA expects and the size of this fine reflects how seriously we view these breaches."
She said the FSA would continue to monitor how firms dealt with PPI redress.
Lloyds agreed to settle at an early date and therefore qualified for a 30 per cent discount. Without this, the fine would have been £6.1m.

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