This is the part about Juliet&Sawyer and Elizabeth from a 2014 interview with Damon Lindelof:

3. Storyline you didn’t think the fans would love, but they did.
Putting Sawyer and Juliet together. The “LeFleur” episode where we essentially said, we’re not going to give the fans the opportunity to see them flirting with each other and developing feelings over time…we’re just going to stuff it down their faces. We’re going to do a time card so like, they basically travel back in time and then the next time we see them, all within in the span of the same episode, they’ve been living amongst the Dharma initiative for a period of time, and they are now together and they are into each other.

And so it was just sort of like, this is not a build. It’s a law. It has happened. We got excited about that story because we loved Elizabeth Mitchell so much, but as we started talking about it, both Josh [Holloway] and Elizabeth were not happy. They were like, ‘Hey guys, we love you, we trust you, but it ain’t gonna work.’ And Elizabeth was just saying, ‘There is just no chemistry between us, I love Josh as a human being but you have done nothing to build this up. You haven’t laid any of the groundwork.’

And we were like, ‘That’s why we love it so much. It just comes out of nowhere. You just have to totally commit!’ And they were like, ‘We’ll do our best.’  And I just started to have that feeling in my stomach like, this is a real show killer. Like, when you put two beloved characters in an intimate relationship with each other and they don’t have chemistry, you end up making the characters look like fools and you can really piss off the audience. Then we saw the episode, and we said, we think this kind of works! But it could be a complete and utter disaster. And it wasn’t until it aired and the audience was like, ‘OK, we are OK with this, we are going to go down this road. We are now accepting Juliet into this sort of love dynamic that was previously only occupied by Jack, Sawyer and Kate.’

Source: E! (September 22, 2014)