You could ask: where did you lose it? You would not ask, 'where had you lost it?' unless you were talking about a situation in the distant past. 'Where did it get lost?' is not something we would really say in this instance...the passive voice is very unnatural here. The other constructions are incorrect. Furthermore, it is not an idiom.

Thank you. But my English teacher told me, When I lose something I should say... -Excuse me. I have a problem. I’ve lost my (something). I might have lost it (somewhere). So I think ‘I’ use ‘have’ sentences, ‘you’ must use ‘have’ ‘had’ sentences isn’t it? A.Where did you lose it? B.I might have lost it (somewhere). is correct response?

Where did you lose it? If someone lost a purse you would say "Where did you lose the purse?" "get lost" is an idiom that you would use to tell someone to go away (most common in America). It is considered rude to say and you would say it if someone is annoying you.