Who do you think left the message on the lighthouse door, the Luteces?
Who killed the man in the lighthouse and left the message on his body to not disappoint them?
The Luteces murdered him. They did it brutally and left the notes to feed into Booker's delusions so Booker wouldn't feel comfortable betraying them and flee to Paris. He even tells Elizabeth that these aren't the sort of people you want to cross.
EDIT:
I'm still totally lost.
Is there no absolute conclusion of what happened or is this where Ken Levine wanted us gamers to discuss our own interpretations?
Here are all the current timelines I've seen of what happened:
Lutece's Perspective of Events:
(my initial one)
(XAL's cleaned up timeline [the end being a yellow alternative universe is the only part where this would be incorrect I'd feel. EDIT: Looking through it again, I don't like some of the things at the start, particularly about Robert Lutece being from Booker's timeline. I'd need to check the date that Elizabeth was taken but I don't see any reason why Robert Lutece would have to be from Booker's timeline, I will have to check when Anna was taken to confirm that Robert Lutece came through before Anna though]) EDIT: Actually, I'm far more skeptical of this timeline than I initially was, Robert Lutece discovers tears at the same time as Rosalind Lutece does. I would use this cautiously, I need to confirm a few things before I can state a huge portion of events are correct since the chromosone slowing him down is definitely incorrect.
Booker's Perspective of Events/Ending Timeline:
(EatChildren's which was then modified by Zkylon to change the beginning section to green instead of yellow; this highlights the looping paradox by showing the loop while showing Booker's entire perspective)
(my version of the paradoxical ending showing why Booker must reject the baptism; the paradox I'm referring to is the paradox visually shown in EatChildren's timeline, it's the red events in this one)
I know it's probably not the written explanation you wished for and I'll explain it in a written format if all of the timelines aren't enough to clear up whatever confusion you have it's just that, by now, it's been asked so many times by people asking for specific segments that it's difficult for me to compile everything in one post since wherever your issue lies with the ending could be in numerous places. Without some specifics of where to start, it could result in a post of significant length that, literally, goes through a significant portion of the entire game's plot.