Wow I must be exceptionally unlucky with my lambskin. :wondering I have a white lambskin Soft Lady Dior Hobo, which after wearing one time for 3 hours managed to get pretty badly scuffed up. It was carried against a black wool dvf dress, and everywhere the dress came in contact with the bag, was scuffed/black. Needless to say, I was not happy.
I brought the bag to Dior for refurbishment, and it returned scuff free, and completely white again. However, the softness of the lambskin was gone, and the quilting was deflated. For the treatment, it seemed like they sprayed some sort of white vinyl-like protection. In hindsight, I probably would have tried LMB first, to see if they could clean/restore the lambskin without it losing it's wonderful qualities (softness & puffiness).
On a positive note, the bag has held up incredibly well since the treatment. It's accompanied me on my travels, stuck to me in 95 degree heat, impervious to sweat and sunscreen. It's pretty much waterproof, and can take any abuse I inadvertently dish out. The coating is beginning to show a little wear/cracks, and I'll probably send it in again soon. I do love my bag, and don't regret the purchase.
Good luck with your purchase, hopefully my experience is only an anomaly.