Gun Song Lyrics
But if I did, you'd be the one
To hold it, aim it, make all of the bad men run
But I don't own a single gun
But if I did I'd break my neck
To please her, make her want to stay in my arms we'd rest
But I don't have a sweetheart yet
It was a pistol, a Smith & Wesson, holy, holy shit
La la la la la la la la la la la la la la
La la la la la la la la la la la la la la
La la la la la la la la la la la la la la
La la la la la la la la la la la la la la la la
La la la la la la la la la la la la la la la la
Some were true and some were wrong
And one day, I pray , I'll be more than my father's son
But I don't own a single gun

From an interview in 2012. http://thedishmaster.com/2012/03/the-lumineers-interview-self-titled-debut-album.html
Is it true that “Gun Song” is about your relationship with your father?
Wesley: My dad had passed away, and his socks were still in his drawer. I went in there to grab black socks, and I pulled out a gun. It made me think of all the things I didn’t know about him. That was the spark of the song.

Anybody know what this song's about?

Following Yokinazu's comment about the song's inspiration, Wes has said finding a pistol in his dad's sock drawer got him thinking about all the things he never knew about his late father who passed away shortly before. I don't think Wes realized how far his father was willing to go to protect his family since we was so surprised to find a gun in the house.
This theme of protection runs through each verse of the song. Finding his dad's gun got Wes thinking about himself and his capacity to protect or stand up for his beliefs, his sweetheart, or his family. Unlike his father, he says he doesn't own a single gun, meaning he's worried he doesn't have the courage to throw a punch or get in the face of all the bad men trying to hurt those he loves. The funny thing is, he doesn't even have a sweetheart to protect. That doesn't stop this young man from worrying about his own capacity to protect or please. It's an anxiety over something that hasn't even happened yet.
When he finds his dad's gun, he begins to reflect on his younger self. Some things he knew were true, some wrong. It's almost like Wes is looking back and asking, why did I spend so much time worrying about finding love? Why was I so worried about protecting a love I didn't have? My father had a family and had a gun to protect them. He was thinking about the right things, but spent too much time worrying instead of taking action. That's what he means when he says he prays to be more than his father's son; to go from the one his father protects to protecting those he loves.