Breeding split to lavender will give you lavender and splits. You will KNOW that any black birds carry a hidden copy of lavender (inherited from their lavender parent).
Breed splits to splits and you wll get lavenders, splits and birds that do not carry lavender at all. No way to tell the difference between those that are split and those that do not carry it at all--basically all non-lavenders should be removed from future lavender breeding, or at least considered blacks, not splits. IFF you get a lavender chick from one of htese parents, if you KNOW the parent, you have identified that bird as a split.
Breed splits to black and you will get splits and blacks, and no way to tell the difference; once again, remove from future lavender breeding.