Most black lambskin Dianas have a Bordeaux interior, like this one here:
If you wanted one with a black interior, there's only one way: you'll have to buy a 4 series bag, which was produced between 1996 to 1999.
Here is the interior of a 4 series Diana:
A collectible series?
The 4 series Diana marks a unique production window where Chanel introduced a monochromatic, all-black aesthetic for select black lambskin and caviar Diana models, matching the interior lining to the exterior leather.
Most people still prefer the Bordeaux interior for the contrast it offers to the black exteriors. But if you're a collector with an eye for rare things, the 4 series Diana might be right up your alley.