This is such a transparently silly concept. Human beings do not mate randomly or even remotely close to randomly. The genes that you inherit are a product of your parents’ choice of mate, not some lottery. Those choices are informed by both biological and cultural factors.
But seriously though, something that happens randomly to you (you don't get to choose your parents) seems similar-enough to a lottery to be used as a metaphor.
It's unambiguously true that no one chose their genes or their childhood environment. That statement doesn't require a metaphysical chooser who might have made the choice.
What's the underlying point you're trying to get across? It doesn't seem like a productive thing to go on about.
> Modern twin studies have concluded that almost all traits are partly influenced by genetic differences.
You seem to be missing the point that we are stuck with who we are. Our mental and physical faculties are handed down to us. We receive them, even though they define us. We experience ourselves.
You have no understanding of basic genetics, why do you think you're in a position to speculate on silliness of metaphors for genetic outcomes?