Jessica Harper, whose £60,000-a-year role included fighting fraud, submitted 93 false and doctored invoices to pay herself £2,463,750.
The 50-year-old gave the money to friends and her three brothers to allow them to buy property.
The fraud took place during the financial crisis when Lloyds received substantial amounts of taxpayers' money.
Harper stole the money over four years by creating a dummy bank account in the name of an IT firm which carried out work for Lloyds.
Southwark Crown Court heard she told police she deserved the money for showing "loyalty" to the firm when she could earn four times as much elsewhere, but denied personally benefiting from the fraud.
"You were a senior employee in the bank in a position with a high degree of trust at a time when Lloyds was substantially supported by a lot of taxpayers' money following difficulties sustained by the bank in the financial crisis," Judge Deborah Taylor told her.
"You disregarded your duties out of a sense of entitlement to take other people's money for your own benefit and that of your family."
Harper, from Croydon, south London, had previously pleaded guilty to a single charge of fraud by abuse of position and a second charge of money laundering over a period of four years.