Ever since "LA X", I've joined probably every other LOST fan in trying to figure out the significance of the Flash-sideways timeline. I still call it an alternate timeline, even though Damon and Carlton don't like that. It's most certainly "alternate" to everything on the show that I'm familiar with, and I have yet to see how it has any connection to what's going on in the "normal" timeline. But I heard Damon and Carlton state that we'll soon learn how it's connected, so I'll just patiently wait for that to be revealed.
In the meantime, I've been trying to figure out what exactly we're seeing in this alternate reality. For whatever reason, the Island is underwater, and people's lives are different as a result. Obviously the Island did exist as recently as the 1970's in this alternate timeline, because we see the DHARMA barracks fully intact at the bottom of the ocean. The best explanation from what we know is that the Jughead detonation caused the Island to sink, and that split the timeline at July 1977. That doesn't explain how Ben and Ethan survived that incident and got off the Island, but obviously they did and continued to live normal lives in the real world.
So going along with this theory that the sinking of the Island in 1977 resulted in Timeline X, how does it explain all the other changes we've seen in the other characters who never had any association with the Island prior to Flight 815? I'm going to attempt to vaguely answer that here.
Jack seems to be more nervous about flying so that Rose is the one to assure him that turbulence is normal, he has a small wound on his neck, his hair is longer, and he can't figure out where he's met Desmond before. The only change in Jack's life that I can see being caused by the Island not existing is that he never met Jacob. I guess somehow Jacob's words to Jack about the Apollo bar needing "a little push" just somehow affected his outlook on life and was enough to affect crucial decisions that made him who he is today. Possibly when Adam Rutherford and Sarah were brought into the E.R. at the same time, Jack chose to save Adam's life instead of Sarah's, so he never had to go through the anguish of performing a miracle spinal surgery on Sarah. And that also means he never met Desmond in the stadium.
Instead of the lottery numbers causing Hurley nothing but bad luck, Hurley considers himself the luckiest man alive. The obvious impact of the sunken Island is that the Numbers were never broadcast in 1988 for Sam and Leonard to hear, so Hurley never became aware of the Numbers and didn't use them in the lottery. But then how did he win the lottery? This also brings up a question that I've had for a while: Why were the winning lottery numbers the Valenzetti numbers in the first place? It couldn't possibly be a coincidence, so somebody already familiar with the numbers had to have somehow staged the lottery, possibly to see if anybody played those numbers. And without the Island in the alternate timeline, this wouldn't have happened, so the winning lottery numbers were different, and by an amazing coincidence, or fate, Hurley still won the lottery with different numbers, but wasn't "cursed".
Without the Island, there's no telling how Desmond's life would've turned out. Maybe Charles Widmore went down with the Island and never had Penny. Maybe Brother Campbell (who we know was associated with Eloise Hawking) never recruited Desmond into the monastery. Even if those changes didn't take place, and Desmond still met and fell in love with Penny and did the solo race around the world, there was no Island to crash on, so he would've completed the race and returned to civilization. What he was doing flying from Sydney to L.A. is anybody's guess. Or was he even really on the plane? Nobody except Jack actually saw him, and then he disappeared without a trace.
In this timeline, Shannon stayed in Sydney instead of coming back with Boone. I mentioned the possibility that Jack saved Adam Rutherford's life instead of Sarah's, so that would've had an effect on Shannon's life and whatever decisions she made.
Sun and Jin
This is another case where the Island's submersion could've prevented a crucial encounter with Jacob. But in this case, the changes in their lives don't really make sense. In the original timeline, Jacob touched them at their wedding. In the alternate timeline, it appears that Jin and Sun are not even married. So something else must've made a difference earlier in their lives. Well, one thing we sort of know is that Sun's father has had dealings with the Hanso Foundation. The destruction of the Island may have caused the Hanso Foundation to go bankrupt, or forced an investigation into what projects it was funding, or caused them to turn their attention elsewhere. Either way, it's possible that it meant that Mr. Paik never became a corrupt businessman. It's hard to tell, since we don't know much yet about Sun and Jin in the alternate timeline.
Sawyer seems a lot more cool-headed and polite than he did in the first season. From the advice he gave Hurley on the plane, he seems to know a thing about people taking advantage of others, so I don't know if he's still a conman, or if he had a different reaction to the death of his parents. This one is trickier to figure out, because his encounter with Jacob happened in 1976, before the Incident, so it's hard to see how the Island's nonexistence could've affected Sawyer's life. Of course, it's still possible that the Island sank before 1977, or that for some reason Jacob never existed in that timeline. Then young James Ford never finished writing his letter and eventually stopped holding a grudge against the real "Sawyer", which led to his much different demeanor. And he flew to Australia for some completely different reason.
Michael and Walt
They weren't on the plane, possibly because the Island never made Walt "special", so Brian Porter never begged Michael to come get Walt when Susan died. That's the best I can come up with for that one.
It seems that he has a decent relationship with his father in the alternate timeline, given that he's still with Helen, and she suggested inviting his father to a Vegas wedding. This is another tough one to figure out. Locke's Jacob touch didn't come until the moment when Locke's father pushed him out the window, and all of Richard Alpert's visits happened long before the Incident. Maybe this is a timeline in which the Losties never travelled to the past, so Locke never told Richard to visit him. Or possibly whatever changed as a result of young James Ford not writing his letter somehow changed something about Anthony Cooper. I don't know, I'm just grabbing at stuff here.
Kate, Sayid, Charlie, Claire
I'm grouping these together, because I don't see any changes in their lives in the alternate timeline. Everything we're seeing with them is what could've happened in the original timeline if Flight 815 had landed in LA. Kate escapes Mars' custody and is on the run again, Sayid is still looking for Nadia, Charlie needs a heroin fix in the lavatory and realizes his life his hopeless and tries to kill himself, and Claire still plans to give up her baby for adoption, only to be met with an unexpected turn of events once she gets there.
As you can probably tell, I'm just desperately trying to make sense of all this flash-sideways stuff, so that it doesn't seem like the pointless side story that it feels like at this point. Damon and Carlton have promised us that there's a significance to it, so I'm just going to continue to trust that we'll find out what it is before the series is over.