If the "blue laced" have the same double lacing, and the same mahogany center in the feathers, then you should be able to interbreed them with the normal double laced ones. If the "splash" also have the double lacing with mahogany, they can be interbred freely as well.
At that point, there is really no reason to prefer blue x blue, or blue x black, or blue x splash. Every one of those will give about 50% blue chicks. Black x splash will give 100% blue chicks, but with no blue among the parents you cannot select for what shade of blue before you hatch the eggs.
Some chicken breeds also have a "blue laced" with chickens that are blue all over, with a black edge (lacing) on the feathers. Blue Andalusians are an example of this. And some some chicken breeds have chickens that are splash all over, with no visible lacing and no gold/red/mahogany colors. Those colorings would not be good to mix in, because even though the blue gene would work right, the feathers would not have the right pattern of lacing around mahogany centers.
But as long as all the chickens have lacing of one color or another (black, blue, or splash), and they have the right mahogany color in the middle of the feathers, you will probably want to breed from the ones with the best lacing, regardless of whether that lacing is black or blue or splash.
You say the blue is a dilution that affects the lacing pattern-- I thought it just affected the color of the lacing (black becomes blue or splash), not the actual pattern (where the color is on the feather.) If the blue gene can change where the colors appear on each feather, then I can't help, because I don't know about that.
Probably the "safest" or most certain way to deal with this is to pick the most perfect birds you can (good blue shade, good lacing pattern) and breed them to each other. Half the chicks will also show blue, with the other half having the wrong colors (black or splash.) This way, at least you can see how the blue affects the birds you are choosing as breeders. And if you find a pair that produces really nice chicks, definitely keep repeating that mating, regardless of whether it fits any prediction of what "should" work well.