According to Reference.com, Lady Justice is blindfolded to represent her impartiality in matters of justice and the law. Her statue is also referred to as Blind Justice and the Scales of Justice.
Lady Justice is a combination of Roman and Greek goddesses: Justitia who was the Roman goddess of justice and Themis who was the Greek goddess that encompasses divine order, law and custom. While statues of these goddesses date back to classical antiquity, the earliest noted representation of her with a blindfold is the Fountain of Justice located in Berne, Switzerland, dating back to 1543. Lady Justice statues are usually found in or near courtrooms and courthouses.