It is definitely different than the other colors of laced chickens, that have a black edge on a gold feather. The gold can be turned to red or silver. Or the black edge can be turned to chocolate or blue or white. For all of those, there are two colors involved and each can be modified by various other genes, which is obviously different than the black-laced-blue we're talking about here.
I'm not sure about the genetics involved, but it appears that some birds do have blue in the middle of each feather, with black or a very dark blue at the edge of the feather.
I don't see that in pictures of black or splash birds, just the blue ones. I'm mostly going by pictures because I haven't seen enough blue chickens in person to draw any useful conclusions. But I'm pretty sure the black-laced-blue ones do exist, unlike some of the other things one sees on the internet.
I've seen speculation that it's just something the blue gene does, and I've seen speculation that maybe such birds have the pattern gene and other genes that would normally make a laced bird, but I haven't seen any conclusive proof either way. Since some birds have this laced effect and others do not, it seems a safe assumption that there are some genes affecting it, but that's not really helpful for figuring out which genes are involved.
Choosing the ones that have the right traits, and breeding them in hopes of getting more, is likely to work as well for that trait as for any other trait.
In this case, it looks like OP needs the blue egg gene, plus a basic understanding of black/blue/splash, plus selection for the exact effect they want in the feathers. From there it should just be a matter of time and patience, to keep selecting and breeding the right birds to get closer and closer to the goal.