What is the "Only one obstacle?"

At the Lutece home, you find the following photograph:

What is the "only one obstacle?"

This answer guesses that it means the lighthouse supervisor, but that seems pretty unlikely...

Solution 1:

Needless to say – SPOILERS AHEAD!

Due to lack of other in-game sources, and seeing that "only one obstacle" was written on a picture of the lighthouse, the "only one obstacle" that the answer you mentioned says (the lighthouse keeper) is the closest possible "obstacle". This is also since the lighthouse keeper maintains and guards the "entrance" to Columbia (the "chair" in the lighthouse). Booker won't be able to go to Columbia unless the Luteces find some way to deal with the lighthouse keeper.

There's a hint in the lighthouse that Comstock ordered the lighthouse keeper to stop Booker from getting to Columbia:
_{Click on image thumbnail below to view larger, original image.}

In the answers to this question: What was up with the coin flip question? - we learned that the "Booker DeWitt" player character is the 123rd Booker DeWitt that attempted the rescue of Elizabeth. All other Bookers that the Luteces assisted in rescuing Elizabeth have failed for some reason. We also learned of constants and variables in the different multiverses. e.g. Booker flipping heads and not "rowing", is a constant, and whether Booker chooses a cage or a bird brooch is a variable.

Why the lighthouse supervisor was the "one last obstacle" will depend whether he is a constant or a variable.

Possible explanation on why the lighthouse keeper is the "only one obstacle" if he's a variable:

[The Lutece twins] tried several scenarios to get Booker to get on that chair of his own volition, and only the one where the lighthouse keeper was killed execution style was the one that worked.

i.e. Booker will only get on the chair if the lighthouse keeper is killed.

^{Source: Comment at Reddit /r/Games subreddit post, "Lingering mysteries of Bioshock Infinite" by Reddit user, Hector_Kur}
If the dead lighthouse keeper is a constant:

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.

i.e. In all universes where the Luteces sent Booker to Columbia to rescue Elizabeth, the "only one obstacle" in getting Booker to Columbia is always the lighthouse keeper.

^{Source: Answer that OP mentioned on the "Who is the dead man in the lighthouse?" question, by @Answergaming}

Solution 2:

Well, my opinion is that the "only one obstacle" refers to getting Booker to Columbia in the first place.

I seriously doubt it could be the dead lighthouse keeper, because he was a last-minute addition to the game, and seems to be completely unrelated to any other plot-points, so it's highly unlikely that they would suddenly also add this one important plot-point related to the lighthouse keeper and not expand on it at all.

Considering Booker had to be rowed to a lighthouse in the middle of nowhere and take a rocket up to Columbia, that actually seems like a pretty big obstacle.