Collider, the Lost writer explained why.
"Ridley [Scott] and I talked at great length during the story process of the first movie about what subsequent movies would be if Prometheus were to be successful" he said in the interview. "And I think that the movie ended in a very specific way that hinted at, or strongly implied that there were going to be continuing adventures worthy of writing stories. What those stories would be would not necessarily usurp or transcend the Alien franchise as we saw it because we know that the Nostromo hasn’t come along yet. So the idea was to set up a universe that… Is it a prequel? Okay. If that’s what we want to call it, sure. But the sequel to this movie is not Alien. The sequel to this movie is this other thing."
He continues, "So Ridley and I talked about what that other thing might be, and he was excited about doing it. But then I think what ended up happening was that the movie came out, and there was a reaction to the movie. And I got really wrapped up in Star Trek, and really wrapped up in this movie that I’m producing and writing with Brad Bird. And I have a TV project that I was really passionate about. Ridley and I had a meeting after Prometheus came out where we started talking again about where this journey would go. And in that meeting I said to him, unfortunately, before he could ask me and go through the discomfort of whether he was going to ask me or not… It’s sort of like having a date where you’re letting the other person know, 'I'm another relationship.' So I can’t tell you that he asked me and I said no. But I did communicate to him that I was working on these other things."
Of course, Lindelof was not the first writer on Prometheus, as he was brought on to re-work the script by Jon Spaihts. "The thing about Prometheus was it was a rewrite. Jon Spaihts wrote a script and I rewrote it. And still it was a year of my life that I spent on Prometheus, kind of all in. The idea of building a sequel to it—from the ground up this time—with Ridley is tremendously exciting. But at the same time, I was like, “Well that’s probably going to be two years of my life.” I can’t do what J.J. [Abrams] does. I don’t have the capability. I’m usually very single-minded creatively. I can only be working on one thing at a time. So I said to him, 'I really don’t think I could start working on this movie until I do this other stuff. And I don’t know when the other stuff is going to be done.' And he was like, 'Well, okay, it’s not like I asked you anyways.' He and I are on excellent terms and it was a dream come true to work with him. But much to the delight of all the fanboys, I don’t see myself being involved in Prometheus-er."
It's fair to say that there wasn't a film out this year that split opinions quite like Prometheus and a lot of the negativity the film received was placed upon Lindelof, so it shouldn't come as a huge surprise that he won't be back for the sequel. We will keep you up to date with any new Prometheus news when it comes in.