The international private banking business will be sold to Union Bancaire for up to £100m.
Initially £65m in cash will be transferred, with the remainder dependent on the unit’s performance.
The private bank is based in Geneva, and will be sold along with its branches in Zurich, Monaco and Gibraltar.
Meanwhile its Dubai international finance centre will be closed, and the group will be withdrawing from South Africa.
And Lloyds is selling its Miami international private banking office to Banco Sabadell for £8m.