Hmm. Since "lucky" appears to be a legitimate translation (see below), seems to me your answer should be accepted. Maybe it wasn't the anticipated translation, but it looks like it should be a valid one. You could report it, if you haven't already.
You could use this as an adjective to describe someone or something. Štastná náhoda, Šťastný Jim, Šťastný Luke - lucky coincidence, Lucky Jim, Lucky Luke.
But it does not really work in "být šťastný", we say "mít štěstí" instead ("to have good luck").
That is the same as saying she is always happy. The Czech double negatives can be very confusing.