For professional and semi-professional publications, writing is considered published if it has previously been made available anywhere. That means Lush and any other website, including personal sites and blogs.
It’s not about whether the writer’s been paid. If thousands of people have seen the story on Lush, then you aren’t able to provide first/exclusive publication rights, which is what many such publications require. In such matters, you can only submit previously published material if a publication’s submission guidelines specifically say so. In the rare cases when this isn’t mentioned, always enquire before submitting.
If you breach a publication’s submission guidelines, the story will almost certainly be rejected without it being read. Plus, the author will become persona non grata if a publication accepts a story, only to discover later they are not getting what they’re paying for. Then you’re talking about contractual issues that are beyond my knowledge.
Hope this helps.