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").