I think I finally figured out my problem with theorizing how time travel works on LOST. All this time, I've been making predictions based on what makes the most logical sense from what we've seen, and that led to a very rigid whatever-happened-happened, the timeline can't be changed even slightly, you can't create another timeline, the Jughead bomb always exploded, etc. So when I watched "LA X" and saw this new "alternate" reality, I just kept on assuming that it was nothing more than a big hypothetical "what if the plane never crashed" side story. After all, it made absolutely no sense that a hydrogen bomb would sink the island and leave structures on the surface intact, or that this would cause changes in characters' lives before Flight 815, like Jack being nervous about flying or Shannon not getting on the plane or Hurley having good luck, so I figured it was just the writers having fun with this hypothetical timeline as a storytelling device. So while it was interesting to watch in the two-hour season premiere, I lost interest in following the "alternate" story beyond that.
The main thing that started to change my mind afterwards was hearing Damon and Carlton stating in multiple interviews that this new timeline was real and somehow related to the continuing 2007 timeline. It still didn't make sense to me at first, but then I finally realized that these writers would much rather create plot devices that tell an interesting story than to restrict themselves to what makes the most logical sense. And for five seasons, they've repeatedly done an excellent job at writing plot twists that completely blow my mind, while also keeping me assured that every mystery has an explanation. So although I haven't seen much indication within the show itself that I should be paying attention to this flash-sideways timeline (except perhaps Juliet's "it worked" dying thought reported by Miles), I'll keep watching with an open mind and wait to see how Damon and Carlton end up resolving the two timelines. I just hope that they do it soon, and not dwell too much on the non-crashing characters' lives after landing at LAX... especially Kate. The last thing I care about right now is seeing what Kate does in the alternate timeline.
Oh, and I do agree with the prediction made by several people here, that at some point, Juliet X will meet Sawyer X and suggest that they get coffee some time and go dutch.