Lloyds TSB Offshore Ltd. said it will open an office in Stamford, its first in the Northeast. The company, a subsidiary of Lloyds TSB Bank, said the new location would provide international and offshore personal banking services to the international community living in the tri-state area. An executive said the new office would provide the company with a presence in the New York metropolitan area, and fill a need for banks to meet the demands of customers who require “borderless banking.”Â