As I missed out on this doll myself I have been asking around to get a decent shot of her and eventually Dagmar managed to get me a photo I could work with. There were only 999 Karl Lagerfeld dolls made and a lot of collectors missed out. I wanted her for her new sculpt, made for this doll. If she will be the one and only one remains to be seen. Other collector dolls made for certain designers have been seen in new releases afterwards so we will keep the fingers crossed. And yes we did! Good thing they didn't make her one of a kind. So far (as of Sept 2015) not many people got their hands on any of them, but I did and as soon as I get my 10th Anniversary Tokidoki Barbie dolls, I will add photos of them here.
There was a lot of talk about this sculpt looking a lot like the new DreamHouse Skipper face and there are a lot of similarities. Since I don't have both dolls on hand to examine I can't really tell what exactly the differences or similarities are. For one thing the Karl face has more angles.

Karl
Copyright: 2013

Doll belongs to/photo taken by and used by permission from Alberto García

BCP92 Karl Lagerfeld, 2014
Photo taken by and used by permission from Dagmar
 

TokiDoki Barbie
Doll belongs to/photo taken by and used by permission from Gerry
 

Andy Warhol Campbell's Barbie
Doll belongs to/photo taken by and used by permission from Gerry
 

DGY08 LOOK - Sweet Tea Barbie
Doll belongs to Eva H

DVP56 LOOK - Pool Chic Barbie, 2015
Doll belongs to Eva H

Doll belongs to Li

DYX63 LOOK - Hipster, 2016
Doll belongs to Li

FJH82 Unicorn Goddess Barbie, 2018 (c2017)
Doll owned/photo taken by Danielle Kempke