Lady or woman in this instance should be accepted. It is correct in English to call a teacher a woman or a lady. It is not like "my lady" which was the old respectful address to adult females in Europe. Man - woman , lady - gentleman. A speaker addresses his/her audience as "ladies and gentlemen."
Yeah, but we have "nő" in the Hungarian sentence. And that is "woman".
"Lady" would be "hölgy".
Strictly speaking. Of course, there are differences in usage. Even in this very course, when they call "cleaning lady" a "takarítóNŐ", not "takarítóhölgy".
"Ladies and gentlemen" is "Hölgyeim és uraim" in Hungarian.