"Lux leather" is not a special term used to describe a certain process for making leather, nor does it refer to a type of leather made from a certain animal. It is simply a way of indicating that the leather goods you are considering purchasing are of "luxury" quality. You may see the term styled as either "lux" or "luxe," depending on the preference of the manufacturer.
There is a company that goes by the name "Leather Lux." Founded by Marianne Labuschagne in 2007, the operation is based predominantly out of Windhoek, Namibia. In addition to handcrafted genuine leather handbags, the company also produces leather rugs -- created with scraps from the handbag creation process -- and wire crafts.
Many types of leather are deserving of the appellation "lux." One such type of leather is clemence, created from tanning the hides of very young bulls. This type of leather is often used to make handbags and wallets for designer labels like Marc Jacobs and Chanel. It is considered luxurious because of the soft and supple texture it possesses. Other luxurious types of leather include togo (made from older bulls), box calf, and Chevre de Coromandel, which is a type of leather made from goat skin.
In addition to luxury apparel and accessories like handbags and wallets, lux leather is used in all kinds of other handmade and manufactured goods. A recent Bugatti car, model Veyron Fbg par Hermes, features interior leather upholstery of the same grade of clemence leather that Hermes uses to make its designer handbags. Fine leather can also be made into stair runners, ink blotters for desks, golf bags, belts and many other items.