Mr Sandler, currently chairman of nationalised Northern Rock, is one of two leading candidates to take over from Sir Victor Blank at Lloyds, in which the taxpayer has invested £15bn and has a 43pc stake. The other is Sir Win Bischoff, the former chairman of Citigroup.
"The chairman of a nationalised, or part-nationalised, bank should not be a non-dom," Lord Oakeshott, Lib Dem Treasury spokesman said. "Ron Sandler should not become chairman of Lloyds."
The Lib Dems opposed the appointment at Northern Rock of Mr Sandler, a former boss of the Lloyds of London insurance market.
He was initially paid £90,000 a month as executive chairman but his salary fell to £350,000 after appointing a chief executive and moving to non-executive.
At Lloyds he would expect to be paid about £600,000.
Mr Sandler attended university and has spent much of his adult life in Britain but was born in Zimbabwe and carries a German passport. As a non-dom, he is only taxed on his UK income and not on overseas income or gains, unlike UK nationals. About 130,000 people in the UK enjoy the status.
UKFI, the body that manages the taxpayer’s stakes in the banks, is unlikely to object to Mr Sandler over his non-dom status. The Government appears to be unconcerned about non-doms despite attempting a tax clampdown on them two years ago. Northern Rock’s former finance director Ann Godbehere was also a non-dom.
Lloyds said it has yet to make an appointment.