We're talking about basic income for the purpose of ending poverty, not giving people a billion dollars every year for some undefined purpose. Your hypothetical is nonsense.
People who win the lottery often end up worse off than when they started. Giving everyone a multiple of the highest lottery winning every year would be destructive.
No your point specifically is nonsense, because its a false comparison. Having a basic billion dollars would be massive wealth redistribution, as opposed to minor, and would have many additional negative consequences due to the severity of it.