This theory ties just about everything together, and I start by shedding light on the two basic questions that were indeed answered during Lost: What is the island? What do the timelines mean for our Losties?
The island is a place on earth with mystical and natural powers. The mystical aspect of the island heals the sick and also offers its inhabitants an opportunity to redeem themselves and absolve their past transgressions. This later point brings us to the MIB and Jacob debate on whether human beings, when given a chance to redeem themselves, can actually do so. Flawed individuals were lured to the island to take part in this game played by MIB and Jacob. In times past, MIB won the debate, but Jacob insisted there was always “progress.”
The natural power of the island enables its inhabitants to transcend space and time through a vortex of electromagnetic forces inside of the island. This is what needed to be protected from everyday people. Imagine the consequences if people were able to travel backward or forward in time! “Mother” understood this, and she was one protector in an ancient line of protectors. Unfortunately, the Dharma initiative discovered the space/time mysteries of the island while Jacob was in charge. They did experiments to see if “what happens, happens,” or whether the alternative is true--destiny is relative and can be changed. These secrets needed to be protected. Richard, the Advisor, through Ben helped seal the Dharma initiative’s fate.
Once “The Others” got rid of the Dharma initiative they were lured into exploiting the island, too, and took up the work the Dharma folks began. The Polar Bears were examples of one of their many experiments. If a Polar Bear was alive in the Arctic in 2004 and transported to a tropical island in 2002, would it still be alive? If it can live on a tropical island in 2002 through 2004, then “what happens, happens” and its destiny and demise has not changed. If the Polar Bear living on the island dies before 2004 (it is shot by Sawyer for example), it demonstrates that destiny can be changed. Remember, too, Charlotte found Polar Bear bones in a dessert and smiled knowingly.
What eventually happened to people who left the island, and to the Losties? Widmore, who was once banished by Ben, came back to the island to exploit it in some way, and he brought the Freighter people in to help him. Eloise understood that destiny can be changed. She worked tirelessly to undo the death of her son, Daniel. Through her manipulation, the Losties who escaped the island were sent back to the island. Some were indeed transported to the past and assisted in changing their destinies, and the destinies of some other island dwellers as well, by detonating jughead in the 1970’s.
How does it all come together? After jughead exploded, the Sideways world showed us the altered lives of our Losties and others—Eloise, Charles, Desmond, Dogen, etc. They have the some of the same basic instincts (Cuse said that they were the same archetype), but their life choices were different due to their subconscious island experiences, and so then were their circumstances. Also, Eloise got to spend time with Daniel and was understandably reluctant to let go again.
Now, I’ll tie in the mystical aspect of the island. Because of the island’s redemptive powers, many of our Losties received the redemption they had earned while on the island. In the end, they were able to travel to a place reserved for the “good” among us. It is also possible that whenever their lives in the original timeline were lost (some were lost before Jack died, some after), their lives in the Sideways timeline were also lost. That is why Jack’s neck was bleeding in the Sideways timeline—his time in both worlds was about up. If the belief that our life flashes before our eyes is true, then it stands to reason that if we lived two lives, they both would pass before us.