Ken Levine, the creative director of Bioshock Infinite, stated in an interview (5:47) that it's the lighthouse keeper.
(Asked while walking up to the dead man in the lighthouse)
Q. How much went into making sure that this wasn't just an empty lighthouse that you're walking up? How much attention went into the writing on the wall (which isn't necessarily legible, but is there as a nice detail)?
A. That was all actually added very very very late, because we didn't really realize how important it was to sell Booker's story in the lighthouse, rather than the story of just going to Columbia. And so this lighthouse keeper, the writing on the wall, the mess, all that got added in the last few weeks (before I came out to show it to you guys), because we realized that story wasn't resonating very well. And little details like, you know, he's got a pillowcase over his head; random killers don't put pillowcases over peoples' heads and shoot them, so this is clearly some kind of professional work.
And so all these details just kept getting added along the way, mostly from having people play it and seeing: were they getting our intent? Were they getting what we were trying to do?
So, apparently the dead body (which even the creative director considers to be just the lighthouse keeper) was just added at the last minute to emphasize the seriousness of Booker's situation, and wasn't meant as an important plot-point.
(Though, they could always figure out a way to work him into the plot in a future DLC :) )
