According to Stephen Hawking, there are plausible explanations for no paradox in time travel:
“A possible way to reconcile time travel, with the fact that we don't seem to have had any visitors from the future, would be to say that it can occur only in the future. In this view, one would say space-time in our past was fixed, because we have observed it, and seen that it is not warped enough, to allow travel into the past.”Carl Sagan made a similar argument during a NOVA interview in the 1990s: “Maybe backward time travel is possible, but only up to the moment that time travel is invented. We haven't invented it yet, so they can't come to us. They can come to as far back as whatever it would be, say A.D. 2300, but not further back in time.”
So, time travel may indeed be possible, but you can’t go back any further than the point at which the time machine was first invented in the space-time line.
This line of reasoning would mean that there would be little chance of a time traveling paradox - - - i.e. going back in time to kill Hitler before World War II. But it also stops future paradoxes since the time traveler would not not what the future holds when he arrives in the future so he cannot change it. But perhaps, his mere presence in the future would cause changes that could alter the future - - - but then, is his arrival already part of that future time line?
The Hawking-Sagan reasoning was not applied in LOST. The characters quickly time skipped to the past (1970s) and to the future-present. There was no logical or systemic way the island took only a few characters along for the time ride, while leaving others in different time periods in the same place. In LOST's time travel loops, it is more likely that there were not truly time-space jumps but hallucinations, simulations, vivid dreams or laboratory rat experiments to challenge and change the main characters behaviors.