Split is another word for heterozygous, but is usually used in the context of a recessive gene. Since the gene is recessive, its presence will not "show" unless the bird is pure for the gene; however, breeding records will (or should) document that the bird carries a hidden copy of the gene. Bred to another bird that is split for the gene or pure for it, a percentage of the offspring will be pure for it, and you will be able to see its presence in those birds.
A lavender split will not give 25% black, 50% blue and 25% lavender. Bred to a pure lavender bird, it will be 50% split, 50% lavender. Bred to another split, you will have 25% lavender, 25% not-lavender and 50% split for lavender--but ou will NOT be able to tell the not-lavender birds apart from the splits.
I am not all that familiar with lemon cuckoo, but cuckoo is not a recessive gene, it is incompletely dominant, and if present in even one copy will show. It is also a sex-linked gene, with females only having one copy. And I do not know which genes for lemon would/could be split, either.