The letter, Lloyds stated, would enable customers to remain informed about the upcoming situation, and help them with their next steps.
Similar correspondence has been received by some customers of Coutts and Barclays.
Nationwide has written to 5,000 customers across the Netherlands and Italy informing them of potential closures.
A spokesperson for the building society recently told Express.co.uk: “As is the case with a number of UK-based financial services providers, due to changing rules regarding UK accounts held by those in some EU territories, customers residing in those areas will no longer be able to use their accounts going forward.
“As such, we have had to write to our members in Italy and the Netherlands to let them know that, as a result of the end of the Brexit transition period on 31 December 2020, we will no longer be able to provide them savings accounts, current accounts or credit cards in their jurisdiction.