I am aware of tenses, but "am lucky and have been lucky" I have felt as same meaning when I read news papers or some books. Could you give some examples for that?
"I am lucky" could be a general statement saying that I am usually a lucky person. Lucky things have probably happened to me over the course of my life. It could also specifically refer to the current time. Perhaps someone just gave me a new car for no reason so right now, at this exact moment, I am lucky.
"I have been lucky" refers to the past but makes no mention of the present.
If you could post some full sentences that you have found, including the context, it will be much easier for us to tell you whether we find any difference in meaning.