They're both usable, but they don't both mean the same thing. They're both casual questions in statement form. The first one is simply asking someone if he lost his luggage.
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PreciousJones (Have) you lost your luggage? and (Did) you lose your luggage?Are both useable and mean the same thing?Thanks!But I'll go with what Avangi says as well. Only thing is my answers are not as creative - yet correct -