Tell me...
Does the Lav gene behave differently when bred with a Blue based bird, as opposed to a Black?
OK, basics of the lavender gene:
Black/black x Lav/lav = 100% Black/Lav splits (look black)
Black/black x Black/black = 100% Black/black
Black/lav split x Lav/lav = 50% Lav/lav and 50% Black/lav split
Black/lav split x Black/lav split = 25% Black/black, 50% Black/Lav split, and 25% Lav/lav (don't do this--you can't tell the regular blacks from the black splits)
Lav/lav x Lav/lav = 100% Lav/lav (do not do more than 2-3 generations in a row due to a gene near the lavender gene that causes very poor feathering of the tail and rear--breed with black/lav split periodically to maintain proper plumage)
It takes two copies of this gene to make a bird appear lavender. Lavender is an autosomal (not sex linked) recessive to black. A black chicken split to lavender (black carrying the lavender gene) looks identical to any other black bird of the breed, with the possible exception of eye color. I know this from personal experience in raising a big hatch of black/lav splits from black roos to lav hens. My black/lav split roo is beetle green black and actually has dark brown eyes like any other black chicken should, though his brothers had lighter eye color. In retrospect, I wish I had kept a lighter-eyed roo for breeding, because I think the exceptional darkness (including the eyes) has made the chicks from my clear lavender hens look more yellowed, which is not desirable. They are still as cute as the dickens and people who aren't breeding don't care, but it's something I intend to fix imminently.
Blue carrying lavender is also going to look exactly like any other blue, except for possibly lighter eye color again. If I bred my black/lav split to blue hens, their blue offspring would have a 50% chance of being split to lav. Since this does not do anything except make it impossible to know which are true BBS hens without lavender, it's not a good idea. If you just want to create layers that you're keeping for yourself, and not selling any of the chicks, then there is nothing unsafe about it. It just makes tracking the genetic background of the birds impossible.
I suspect the same will be true of splash. What is the usual eye color of splash chickens? If dark, then the lav gene might lighten it. If already light or medium, then there would be no visible difference. However, you can't use eye color as a marker for the lavender gene. There are lots of black/lav splits with perfect dark eye color.
We keep going around about this, but if you really want to confirmation, just plug it into the chicken color calculator. It won't show you what the birds may carry, just what the offspring of a specific mating will look like, and in what proportions.
Just so my blue hens don't forget what it's like to be with a roo, they spend time with my black/lav split guy, but as soon as I have a blue roo, that will stop and I will return him to full-time duty with the lavs only.
My first blues are hatching right now. They are from eggs collected from my blue hens when they were with their previous regular black rooster. I'll probably keep every blue chick that hatches from them, since it's a chance to bring in that other roo's genes into my flock. Might even keep a black or two. I only have one pure black Orp hen now so that I have a different line to use to make black/lav splits (as well as blues, depending on what roo I put her with).
I can't wait for my first two to get dry. Their down does not appear much different from lavenders (wet). I'll have separate brooders for my lavs and black/lav splits, and for my blues and true blacks. I do not want to go crazy trying to figure out the impossible, especially with the blacks and black splits.