Translation:The old lady is wearing a nice dress.
To my Midwestern U.S. ears, even describing someone as an "old lady" is disrespectful. Also, some men will use it to refer to their wives, but show their disregard for them when they do so. If you insist on using "lady," I would suggest "elderly lady" for the English translation.
When you have an adjective before a definite noun, you have to use the double definite -- both the front article (the separate word: den, det, or de) and the back article (the suffix on the noun). When you have no adjective, you simply use the suffix on the noun, without the front article.