How do you say goodbye and good luck young lady in Italian?

Arrivederci/addio e Buona fortuna ragazza/signorina.

Giovane donna, the literal translation of young lady is also correct but it sounds stilted here. Addio is a more definitive salutation, like farewell in English. Dio is God, a means to, so it literally means 'to god'. Arrivederci is like goodbye and is more formal than ciao. A-(r)ri-vederci=to-again-to see-(to) us. Signorina is more formal than ragazza (girl). Signorina means piccola signora (little lady), -ina makes a diminutive and corresponds to young. Fortuna means luck, you have this word in English too, but you use only to mean destiny, fate: fortune. Fortunate is fortunato in Italian.