Is there some special method or unique way that you lost your passport?
Either the way or method doesn't matter actually. Who care for the way.
Don't lose your passport;I did it last summer.
Is this sentence wrong as well?
Does it mean how something was done? I don't think so.
I thought that an oversight had happened but it turned to your saying it wasn't the case.
Anyway the distinction between the sentence without "it" and with "it" is still strange to me.
Is it about the difference between Am E and Br E, maybe?
I had been so many times warned about my missing the "it" in similar sentences that I can't easily accept your explanation.
How to say the sentence
Don't lose your passport as I did last summer.
using the passive voice?
Don't use your passport as happened to me last year. or (What's the subject in the latter clause?)
Don't use your passport as it happened to me last year.