Lavender cuckoo male x Lavender female will get you Lavender Cuckoo females and single-factor-barred Lavender males. Essentially the males will have similar barring to the females instead of having lighter barring like a pure Lavender Cuckoo male.
Lavender male x Lavender Cuckoo female will make sexlinks, Lavender females and single-factor-barred Lavender males. In theory, the male chicks will hatch with a spot on the back of their heads and the females will be lacking that spot, but since Lavender chick down can be quite pale I can't tell you for sure how visible that will actually be.
As for adding a Barred male to Lavender and Lavender Cuckoo hens, you can do that, but keep in mind that Lavender is recessive so all chicks out of them will be carrying the gene without expressing it. The same gene that causes the cuckoo pattern on the Lavender Cuckoos causes the barring on Barreds.
So Barred male x Lavender Cuckoo female will make all black Barred offspring, all carrying lavender.
Barred male x Lavender female will make black Barred females carrying lavender, and black single-factor-barred or dark-barred males carrying lavender.
