Sorry, Duolingo, but you should accept "this woman." No one in common speech would say "lady."
I thought that the article was omitted when describing a person's profession, i.e. not " Cette dame est une cuisiniere" but simply, "Cette dame est cuisiniere".
When there's an adjective you have to go back to using the article. (An exception to the exception to the rule!)
Since it is a lady we are talking about, would not "Parisienne" be the more appropriate and polite word to use, as in "That lady is a Parisienne cook."? Conversely, "Ce monsieur est un cuisinier parisien." would be "That gentleman is a Parisian cook."
parisian is an adjective and as such does not take a gender a parisian lady and a parisian gentleman. Parisienne is French and parisian is English!
If you were to visit the Oxford English Dictionary you would see this;
Definition of Parisienne in English:
Parisienne noun A Parisian girl or woman. adjective Relating to Paris; Parisian. ‘the most famous Parisienne brasserie in the world’ ‘Parisienne haute couture’ Origin Mid 17th century: French, feminine of parisien ‘Parisian’.
It's not the normal word in English, and you wouldn't use it normally.
...which is to say, it's a word primarily used by pretentious English speakers trying to seem 'haute' by pretending to know or be French.
Probably my friend but as we are all starting from scratch with this new system may be it is better to keep it simple .You are referring to famous Parisiennes and this cook apparently is not a head chef.