I think 'I lose myself', which is present tense, would be 'mi perdo'. 'Mi sono perso' is a passato prossimo, so it would translate as 'I have lost myself', but Duolingo often translates the passato prossimo (for sound reasons, I presume) as a past tense: 'I lost myself'. Translating idiomatically rather than literally, that leaves us with 'I got lost' or, indeed, 'I am lost'.
From what I can tell, "Mi sono perso" can mean both "I am lost" and also "I was lost".
If you think about it, being lost implies an 'event' which has already happened .. the actual getting lost part, the point at which you started to feel lost .. which I guess is why Passato Prossimo is used?
If you want to emphasise that this was something in the past, you can use the imperfect tense and say "Mi ero perso" instead though .. as in, I was lost (at some time in the past)
Yeah, I think that makes sense. Is it a reflexive verb? I just saw that somebody posted this (http://italian.about.com/od/verbs/a/italian-verbs-reflexive.htm) on another page.