The bank, which has branches in Wakefield, Castleford, Pontefract and South Elmsall, will shed 9,000 jobs, around 10 per cent of the workforce.
More than 30,000 jobs have already been lost at the banking group, which is a quarter owned by the taxpayer, since the financial crisis in 2008.
The unite union, which represents staff at the company, called on Lloyds to guarantee there would be no compulsory redundancies.
Unite national officer Rob MacGregor said executive pay should be cut if customer service was to suffer and jobs would be lost.
He said: “Job cuts of approximately 10 per cent could have unknown consequences on customer service and will put even more pressure on staff who have helped get the bank back on the right track.
“The wallets of top executives at Lloyds should not be getting fat by forcing low paid workers onto the dole.”
A Lloyds spokesman said it was not yet known which branches would close.
Lloyds has branches on Westgate, Wakefield, Carlton Street, Castleford, Ropergate, Pontefract and Barnsley Road, South Elmsall.