Actions in Blue Lacuna feel like they have more narrative weight than they do in a lot of IF, suggesting to me that the story might branch at some point. I haven't heard one way or the other whether it does, though, and it feels like learning about the number of endings is probably the best way to find out. How many endings does it have? (I'm referring here mainly to "successful" endings wherein the story can be considered complete; if you can die a dozen different ways before the end of the story, I'd argue that that's at most one ending.)
It has three different endings, each one harder to get than the previous. Each one can be achieved through different group of puzzles.