In Czech "Lady" = "dáma" https://en-cs.dict.cc/?s=lady
And, also, in English "woman" can be definitely used when speaking about, well, women. Just as "man/men" is used when speaking about men. As in: "There were many women at the meeting." or " The boss is a woman." There is even a book titled "Little women" by Louisa May Alcott (1832–1888). An author who was a woman. https://en.wikipedia.org/wiki/Little_Women
I am also confused.:-(
If I understand your message, it says (1) that you needed to translate from Czech to English; (2) that your English translation was not accepted; and (3) that the system responded to the English sentence that you wrote by saying that you should have used one Czech word rather than another. Can you try to explain this again?
There might be a Duolingo technical problem present. However, it would be much more helpful if you used the report button. Normally, the translations behave as they should in a few days and it has been 5 months since the last change. So really, we need your reports using the button, the discussion is not to be used for them and is too unreliable.