To 60% LTV customers can take out 2-year fixes at 1.94% with no fee and 1.54% with a £999 fee.
Andy Hulme, mortgages director at Lloyds Bank, said: "These new rates are a great option for those looking to save money on their monthly payments when remortgaging.
“Many people, particularly those on standard variable rates, could save money by fixing their mortgage payments.
Lloyds also offers customers who move their mortgage £500 cashback towards any costs they may incur.