지는 = who loses or losing (present tense)
진 = who lost or having lost (past tense)
A losing person = a person who loses/is losing = 지는 사람
A lost person = a person who lost = 진 사람
Both are used to describe "a loser". The present tense indicates the person is currently losing; while the past tense describes "losing" as part of his attributes.
Also, "a lost person" can have different meanings in English: a missing person; a person who lost his way; ... Koreans use different words (verbs/adjectives) for each case.