A thousand years in one piece of silverShe took it from his lily-white hand Showed no fear--she'd seen the thing In the young men's wing at Sloan-KetteringThese lyrics are very telling. It is likely that Johanna is picking up a ring that is very old, and probably passed down generations. She is getting the ring because the holder of the ring has died of cancer. I know this because "lily white hand" means really white and Sloan-Kettering is a cancer center in New York. I think it is Johanna's brother who has died because the person is young.
His Honor drove southward seeking exotica Down to the pueblo huts of New MexicoCut his teeth on turquoise harmonicasOh-oh-oh
These lyrics are some sort of flashback. His Honor knows that he will die soon and wants to do something fun beforehand, this is why he goes to New Mexico. We know that he is really close to death because he is so weak that he cuts his teeth while playing a harmonica.
Half of the ring lies here with meThis part shows how upset Johanna is about losing this person. She was so upset that she cut the ring in half and threw it into some body of water to try and forget about this tragic death. She couldn't bring herself to get rid of the entire ring though she she gave it to the narrator of the song. We know this because the word "me". The narrator is probably one of Johanna's friends. The last bit of the song talks about raincoats coming and what I got from this was that raincoats represent Johanna's mood: depressed and dreary, like a rainy day. I don't think A-Punk has an overarching theme, I think it is just telling a story and you really need to take the song apart line by line to understand it.
But the other half's at the bottom of the sea