Because of those genetics, you were not going to end up with a lavender unless both snakes carry the lavender gene.
A striped snow carries the genes for stripe, anery, and amel in homozygous form. This means that it has two copies of the stripe gene, two copies of the anery gene, and two copies of the amel gene. It takes two copies of these genes for the animal to visually display the trait. If they had only one copy of a gene, they would be able to make offspring that show the trait, but would not show it themselves.
And it's the same for the anery motley. It has two copies of anery and two of motley. The two copies of anery match up in each snake, which means the snake MUST be at least an anery. Motley and Stripe take up the same location, genetically. Your snake got one stripe gene, and one motley gene and because they fill up the spots, they make the animal display a morph. Genetically your snake is a motley/stripe. Phenotypically (how it looks) it is a motley. It looks like a ghost motley to me, which means both parents might be het for hypo. But I could be wrong and it might be an anery motley. You'd have to test breed to be sure.
Your snake is also het for amel. It is carrying the gene, because it got 1 gene from the snow for amel. But the anery motley did not give it an amel gene, so it is not displaying amelanism. If you bred it to a snow stripe, you could get anery motleys, anery stripes, snow motleys and snow stripes.
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