I wouldn't! That's just, well... anyway, if I HAD to, I'd probably use strobes, key, shoot-through umbrella 90 degrees image left, and fill 1 - 1.5 stops below 60 degrees camera right. The lighting is very basic, it's the post processing that's giving these images their rather "unique" style.
Overhead incandescent fixtures with a big,big window off to one side, with a yellowish, gauzy sheer over it. Those photos you linked us to have that low-level, untrained, "bleeeech!" aesthetic. They look absolutely awful. Tirediron using the word "unique" and "style" within the same sentence in his post was a kindness. I know, I know, if somebody will pay for work like that, then it's viable work, but still, it looks like total cr@p to me.
I think they're all using different lighting from each other.
The top one looks like simple split lighting, one key way off to the side, fill on the other side, blah blah whatever.
If you look at her nose shadow in second one, you can tell the light is not perfectly to the side. it's like 45 degrees maybe even around toward the camera, but still is really directional. I'd guess a softbox, possibly with grids attached, as a key.
The last one looks like it has separate keys for each person. it could just be her hair blocking the main light so that the fill becomes her key, but I dunno... they may also be using very constrained directional lights or something for each of them.
I think the photos look perfectly fine, personally. Dunno what everybody is retching about. They aren't pullitzer prize winners, but they are fine portraits for showing off clothes *shrug*
I would light my subjects and capture an image that looked good....don't like these sorry lol. All 3 though seem to have a key light with a reflector there isn't any serious shadow. The second image looks like the main light source is pretty close to the subjects.