Where is the lost luggage office?
'Smarriti' — 'smar-RI-ti'. Three syllables; double 'r'; stress on second syllable. It means 'lost'.
Ask any airport staff member, information desk, or fellow passenger when you cannot locate the lost luggage desk after leaving the carousel.
'Dov'è' is a contraction of 'dove + è' (where is). 'L'ufficio bagagli smarriti' is the lost luggage office. This department may be staffed by the airline, airport authority, or a handling agent depending on the airport.
C'è un ufficio per i bagagli persi?
Is there an office for lost bags?
Alternative phrasing; 'persi' is a synonym of 'smarriti'.
Dove devo andare per un bagaglio non arrivato?
Where do I go for luggage that hasn't arrived?
More descriptive; explains your situation while asking.
Chi gestisce i bagagli smarriti qui?
Who handles lost luggage here?
Asks which organisation is responsible.
At Rome Fiumicino and Milan Malpensa, the lost luggage desks are operated jointly by airport handling companies (Alitalia Handler, Swissport, etc.) and are always open. At smaller airports they may be shared with the check-in counter and have limited hours.