In Lost TV series, Daniel Faraday's mother (Eloise Hawking) meets the losties who want to return to the island. How does she know what flight they have to catch to "crash" again and return. What's the point? Is there another island's rule that put her in charge of doing this? Or it's just a scientific way to make them "let go" the reality they're attached to? Why instead, Faraday's father (Widmore) has to put so much effort to find this island?
According to the article about the flight on lostpedia
Essentially, the island is constantly moving and shifting around (which is what makes it so elusive). In order to get the Oceanic 6 back to the island, they needed a flight who's path would match up perfectly with where the island would be so that they can crash it onto the island to return.
There is no island rule about this having to be the flight but merely the only way to keep the island "stable" enough to save it is to have the original/remaining candidates back onto the island in order to stop it from producing the time flashes so sporadically.
Eloise is merely the one that runs The Lamp Post station which it's purpose is to detect where the island currently resides and where it will be.
Faraday's father, Widmore turns out to be the original "others" leader back in the 1950s. And since Ben banished him when he came of age, he's been desperately trying to get back to the island ever since. I'm sure anyone ejected from their longtime home that is constantly moving around the world would be pretty determined to get back at any cost.
Another part of it was also "re-creating" the conditions of Oceanic 815. But it had everything to do with the Lamp Post being a place that find the limited window of opportunity to get back to the island.