Hi there, welcome to BYC!
Also... from your first cross that gives you all black split to lav... when you breed those back to lav, will get lav offspring. Or bred back to each other... will give 50% black and 50% lav.
I'm going to partly agree with the previous poster... but note that I DO intend on using blue with my Lavs...

expecting it breed the same way black does...

Yes, I do consider myself to be a breeder not a multiplier.. and am no stranger to project colors... but still have TONS to learn about genetics... and not saying all my ideas are good!
Whether you choose to call it lavender or self blue may depend on the breed and if it's been accepted into their standard of perfection already, and which one they agreed upon. I haven't worked with Cochin, so am not aware of their preference.
I think aside from just color... it would be nice to know how the frizzle cross smooth will present in the offspring... or will it?!
@The Moonshiner,
@sylviethecochin @nicalandia might any of you be able to offer a complete answer for the OP and maybe even comment about my lav cross blue intent and what the fallout might be? TIA!