Genotype BB DD. A true breeding variety. The Lavender (aka Self Blue) is the result of black and dominant slate in homozygous form.
Here's some additional info. on the history of the slate by Franklin Albertsen:
With slates, we get an additive dilution effect with a homozygous slate (carrying 2 doses) being much lighter than a heterozygote. These light black-based slates are a very uniform pale bluish-grey free of any flecks in the down at hatch. Hence the name, "Blue," which was originally put on them. However, these individuals when mature were somewhat paler in color than what appears to have been desired in the standard originally. The hens are particularly attractive with a uniform grey color with faint white edging on the breast feathers.
The toms are not as pleasing in appearance as hens. A dark edging on the feathers sometimes creates an uneven, blotchy appearance, even though they are free of the black flecks of the heterozygous blue splashes. Some toms were more uniform than others, and careful selection for many years by the dedicated old breeders for, or against, minor modifying factors successfully produced more uniformly colored blue strains. These lighter-colored, clear-feathered strains bred true. About this time, Marsden and Martins' book stimulated the switch from bronze base to black base slates to fit the Standard, but in those early editions, they described the Standard slates and these new blues separately while suggesting the blue would be an acceptable show slate.