The British-born actress, who famously played Tippi Hedren's daughter in The Birds, reveals she was in England ready to start work on the film when she discovered she would be playing Lambert in the project, and Sigourney Weaver had been given the lead.
She tells WENN, "I had no idea because I had only read for Ripley and when I got over to England they called up and said, 'Can you go in for wardrobe for Lambert?' I went, 'Oh no, I'm Ripley.'
"I had to call my agent and he said, 'No, you're Ripley.' It was so bizarre and so I had to re-read the script from the point of view of Lambert, and I thought she was a bit of a whiny b**ch, but I think she became the voice of the audience; she was the only sane character, if you think about it."
The role won Cartwright acclaim and a Best Supporting Actress Saturn Award, but she has never had an explanation as to why she didn't end up playing Ripley.
She adds, "Nobody said anything. I guess I must have misunderstood. I brought it up a couple of times."
The actress, who has just wrapped new thriller InSight with Christopher Lloyd and Sean Patrick Flanery, reveals there were plenty of odd moments during the making of the Ridley Scott classic that spoiled the filmmaking experience for her.
She explains, "If you've ever seen the big box set (DVD of Alien) there are nine outtakes and I'm in eight of them. I had a big part in that movie and it was changed, and I'm glad in the Director's Cut (version) they put the hit back in. I just thought Ripley was an a**hole for not letting us in. How dare she. And when I hit her, that felt like it was spontaneous and it's something Lambert would have done.
"Then, when I was doing publicity for the film, I was asked, 'How does it feel to have the (alien's) tail going up between my legs?' Well, they weren't even my legs. They never shot my death... I kept saying, 'When are we going to shoot that?'"
But Scott chose another actor to double for Cartwright on the day of the shoot.
She says, "I was a little p**sed off."