Who is the dead man in the lighthouse?
Solution 1:
I think I got the answer, and if you think about it, it's quite straightforward. It isn't Booker, or any metaphysical representation of his psyche.
The lighthouse serves as an entrance to Columbia, and as we see at the beginning of the game, used by pilgrims and newcomers that have been accepted into the city. Such a place would have a keeper, a guardian. There are religious motifs all over the place, because as any good Columbian, he'd be a believer. There are charts in the lighthouse that show where the city is going to be depending on the time of the year, and the pattern it follows.
And to activate the chair that ejects you into the city, you need a password, the bell combination, that only said lighthouse guardian would know. Now, in the Lutece labs, you find a picture of the lighthouse with a red circle marked around it and the words "ONLY ONE OBSTACLE" next to it. Their plan was to send Booker through the lighthouse, and the only obstacle was the man guarding it himself.
So that's it. The Lutece have shown to be quite cold in their behavior and not care much about other people's lives when they get between them and their experiments. Maybe they didn't do the deed themselves, they might've just hired another nameless thug to do the dirty job.
But basically: It's nobody but the Lighthouse keeper, who's been tortured and murdered in order to get the means for Booker to get into the city. They might've left the "Don't dissapoint us" message to add color or feed him the idea that he's working for some shady criminal organization.
Solution 2:
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 :) )
Solution 3:
SPOILERS AHEAD!
It can't be Booker, on the basis that I crouched down and looked at his right hand, there's no AD on it, if it was Booker intended by the developers, they would have put it there so that only people playing through the second time would understand the importance of hiding something subtle yet easily missed by a first time player, such as the AD mark.
Solution 4:
MASSIVE SPOILERS - DON'T READ THIS IF YOU HAVEN'T COMPLETED THE GAME YET
Well, it can't be the last guy sent after Elizabeth, cause that would be Booker himself (albeit a version of him from a different reality) - plus, that guy was obviously killed where he sat, so it's safe to say it was the lighthouse supervisor.
More interesting than that is the question who killed him and planted all the "motivationals" like "Don't disappoint us". Couldn't have been the Lutece's (at least not the killing) because they were afraid that interfering directly would mess up reality as a whole - otherwise, they would have freed Elizabeth and/or killed Comstock themselves.
So, maybe Booker halucinated all of that to support his new, fictional memories? After all: "The mind of the subject will desperately struggle to create memories where none exist."
– Rosalind Lutece