Quote: "Brown Red + Blue = Lemon Blue"
Problem here is that the blue does not have the birchen pattern that the lemon blue has. So chances of getting completely properly patterned lemon blues from the first mating are not great. You will get about half that are blue diluted.
The same things goes for the "Black Breasted Red + Blue = Blue Red" Not perfect patterning in the first generation, but about half will inherit blue.
Blue mille fleur is basically the same--you need to breed the blue gene into the mille fleurs. Breeding that in is easy, breeding back all the additional genes needed takes time. Because so many genes are involved, it is more complicated.
While lavender birds can have some issues, dying like you describe should not be a problem. I would suggest getting some unrelated birds of the varieties you are using, keep them separate from the ones with dying issues, and try breeding those unrelated birds together. My guess is that there is either an inbreeding issue or a disease issue (reason to keep them entirely separate). You should also check the chicks you have for lice or mites--they can kill young birds rapidly.
The white mottles are caused by the mottle gene, not the pattern gene, and it is indeed recessive, needing two copies to show in adult plumage. With one copy it sometimes shows in chick plumage, but disappears as the bird grows adult feathers. The pattern gene is dominant, not recessive.