http://www.thefreedictionary.com/High+liver Apparently it means someone who has a nice diet. I have never once in my life heard it used that way though. If you called me a high liver, I would have no idea what you meant. Hope that helps.

Never heard of it. It's not even in the Urban Dictionary. Where did you hear it? Or what's the context?

In different cultures, for example Persian, "my liver" or "hi liver," is a term of endearment. It's addressing the heart and soul of a person. In English it's just an internal organ. :)

According to the free dictionary it means: "one who indulges in a rich diet." It is definitely not a form of address.

I have never heard of this before but on first glance I thought...someone who lives richly. For example: lives in the most expensive house, drinks the most expensive wine, wears the most expensive clothes, and drives the most expensive cars. I don't know where you heard it but it is NOT a common English phrase.